CHAPTER: Polynomials
Important
Questions for SLC
A. Short Answer
Questions
1.
Evaluate f(x).g(x) for the following.
a.
f(x) = x+4 g(x) = x+6
b.
f(x) = x2-2x+1 g(x) = x-1
c.
f(x) = 3x2+6x+4 g(x) = 4x2+x-2
2.
Divide f(x) by g(x) for the following:
a.
f(x) = x3+6x2+10x+16
and g(x) = x+3
b.
f(x) = x4+1 and g(x) = x-1
3.
Define remainder theorem and find the
remainder when 2x3 – 7x2 +5x + 4 is divided by x – 3
4.
Define factor theorem. Is x – 2 a factor
of f(x) = x3 – 6x2 +11x – 6?
5.
Use synthetic division method to divide
f(x) by g(x) in the following:
a.
f(x) = x4+1 & g(x) = x-1
b.
f(x) = 2x3-10x2+19x-10
& g(x) = x -
c.
f(x) = (6x2 - 7x + 12) &
g(x) = (x - 2)
d.
f(x) = (3x4 - 8x2
- 20) & g(x) = (x2 - 2)
e.
f(x) = (2x3 - 9x2
+ 4x - 6 ) & g(x) = ( 2x - 3)
f.
f(x) = (2x3 + 3x2
- 4x - 5) & g(x) =
g.
f(x) = (2x4 - 7x3
- 4x - 5) & g(x) = (x - 3)
h.
f(x) = (4x4 - 3x3
+ 2x - 6) & g(x) = ( x - 2)
i.
f(x) = (6x4 - 5x3
+ 7x2 - 3x + 2) & g(x) = x2 – 2
6.
Use remainder theorem to find remainder
when f(x) = x3-6x2+11x-6 is divided by
a.
x-1
b.
x-4
c.
x+2
d.
3x – 5
e.
5x + 7
f.
3x + 11
7.
If x -1 is a factor of a2 x2-3ax+3a-1,
find the value of a
8.
Find the value of k if the polynomial 3x3+
kx2+x-2 leave a remainder 7.
9.
x – 1 is the factor of g(x) = x2+bx+2.
Is x – 2 the factor of g(x)?
10.
For what values of a will 3x5
+ 9x4 - 5x2 - 4ax + 3a2 contain x - 1 as a
factor?
11.
Find the value of for a for which x7
+ 9x4 - 7x3 + 11ax + 5a2 may contain (x + 1)
as a factor.
12.
Find the values of the polynomial f(x) =
2x3 - 5x2 + x + 2 at x = 0, 1, 2, 3.What are
the factors of f(x)?
13.
Show that 2x + 4 is a factor of f(x) =
x(x + 1) (x + 3) (x + 4) - 4
14.
If f(x) = 2x4 - 3x2+6x
+ k & f(1) = 0 then find the value of k.
15.
What must be added to x3-3x2+4x-15
to make it exactly divisible by x – 3?
B.
Long Answer Questions
16.
State and prove factor theorem.
17.
State and prove remainder theorem.
18.
If x -1 is a factor of a2 x2-3ax+3a-1,
find the value of a
19.
Factorize the following & solve each
of them when they are equated to zero
a.
x3+2x2-5x-6
b.
x3-9x2+26x-24
c.
x2 + 4x2 + x – 6
d.
3x2 + 13x + 12
e.
x3 - 9x2 + 24x –
20
f.
x3 + 2x2 - 5x – 6
g.
x3 - 4x2 + x + 6
h.
x(x+1)(x + 3) (x + 4) – 4
i.
x3 - 13 x - 12
j.
6x3 + 7x2 - x – 2
k.
x3 + 3x2 - 9x + 5
l.
(x - 1)( x - 3)( x - 5)(x - 7) + 16
m.
x3 + 2x2 - 5x – 6
n.
x4 - x3 - 19x2
+ 49x – 30
o.
x3-6x2+11x-6=0
20.
Solve the following polynomial
equations:
a.
x4-4x3-x2+16x-12
= 0
b.
x3-2ax2-a2x+2a3 = 0
c.
x3-7x2+7x+15= 0
d.
x3 - 9x2 + 23x -
15 = 0
e.
x3 + 5x2 - 2x -
24 = 0
f.
5x2 - 23x + 12 = 0
g.
2x4 - 17x3 + 37x2
- 7x - 15 = 0
h.
x3 - 6x2 + 3x +
10 = 0
i.
8x3 – 12x2 -2x + 3
= 0
j.
y = x3 – 4x2 + x +
8 & y = 2
CHAPTER: SETS
Important Questions for SLC
----------------------------------------------------------------------------------------------------------------
1.
If
n(A) = 40, n(B) = 50 / n(AÇB) = 15, find the value of n(AÈB)
2.
n(U)
= 80, n(P) = 50, n(Q) = 30 /
n(PÇQ) =
10. Draw the Venn diagram to illustrate the above information and find the
value of n(PÈQ).
3.
If
n(A) = 45, n(B) = 65 & n(AÈB) = 85 then
a.
Find
the value of n(AÇB)
b.
Find
the value of n0 (B)
c.
Show
it in venndiagram.
4.
A survey conducted shows that 75% like
milk and 60% like curd. If they like atleast one of them then]
a.
Show
it in a Venn diagram.
b.
What
percent were there, who like both?
c.
What
was the percent, who like curd only?
5.
In
survey of 170 girls it was found that 18 girls can neither dance nor can sing,
96 can dance and 69 can sing. By representing these information in a Venn
diagram, find the number of girls who can both dance and sing.
6.
Out
of 100 students, 80 passed in science, 71 in Mathematics, 10 failed in both
subjects and 7 didn't appear in an examination. Find the number of students who
passed in both subject using venn diagram.
7.
In
a survey of 120 students, it was found that 17 drink neither tea nor coffee. 88
drink tea and 26 drink coffee. By drawing Venn-diagram, find out the number of
students who drink both tea and coffee.
8.
In
a survey of 2400 tourists visited in Nepal
a.
Represent
the above information in a Venn-diagram.
b.
How
many were there who liked to visit both places?
c.
How
many were there who liked to visit Bhaktapur only?
9.
In
a survey of 2000 tourists visited in Nepal
a.
Represent
the above information in a venn-diagram
b.
How
many were there who like to visit both places?
c.
How
many were there who liked to visit janakpur only ?
10. In a school of 80 students of class X
were asked what they would like milk or tea 60 said they would like tea, 50
said they would like milk and 10 said they would like neither milk nor tea. By
drawing Venn-diagram, find the number of students.
a.
(Who
like both tea and milk?)
b.
(Who
like milk only?)
c.
(Who
like tea only?)
11. In a survey of group 100 students 55
like to read Muna magazine, 45 like Yuba Manch and 14 do not like to read
either of them, Draw a Venn diagram and give of answer to the following How
many of them like to read
a.
Muna
magazine only
b.
Yuba
Manch only.
c.
Both
of them.
12. In a survey of 60 students, 30 drink
milk, 25 drink curd and 10 drink milk as well as curd then
a.
Draw
a venn -diagram of above information.
b.
Find
the number of students who drink neither of them.
13. Out of 100 students in a S.L.C.
Examination, 80 passed in math, 60 passed in science and 50 passed in both
subjects.
a.
Draw
a Venn diagram to illustrate the above information
b.
Find
the number of students failed in both subjects.
14. In a class of 25 students, 17 like
Volleyball, 15 like Basketball and 10 like both games, Illustrate it with a
Venn-diagram and find the number of students who don't like any of the games
15. In a survey of 200 students 125 liked
to admit in science faculty, 100 in humanity faculty and 40 like to admit
either of faculties and the rest were found not to be admitted in both
faculties.
a.
Show
the above information in a venn diagram.
b.
Find
how many were there who don't like to admit in both faculties.
16. Out of 5000 Japanese who are on Nepal tour, 40% have already toured India 30% have also toured Pakistan
17. Out of 1350 candidate 600 passed in
Health, 700 in social, 350 in Nepali and 50 did not passed in all three
subjects. If 200 passed in Health and social, 150 in Health and Nepali, 100 in
social and Nepali.
a.
How
many candidates passed in all subjects?
b.
Illustrate
the above information in a Venn-diagram.
18. G, S & K represent the people who
read Gorkhapatra, Samacharpatra & the Kantipur daily. If n(GÈSÈK) = 100%, n(G) = 50%, n(S) = 55% n(K)
= 35%, n(GÇS)
= 15, n(SÇK)
= 10%, n(GÇK)
= 20%, then what percentage of the people read all these three daily papers?
19. Of the total candidates in an
examination, 40% students passed in math 45% in science and 55% in Health. If 10%
passed in math and science, 20% in science & Health and 15% in Health and
Maths.
a.
Draw
a Venn-diagram to show the above information
b.
Calculate
the percentage. Who passed in all three subjects?
20. If n(A) = 65, n(B) = 50, n(C) = (AÇB)
= 25, n(BÇC) = 20, n(CÇA)
= 15, n(AÇBÇC) = 5 and n(U) = 100, find the value
of n(
)
)
21. In a survey of 100 people 65 read
Kantipur, 45 read Gorkhapatra, 40 read Himalayan times, 25 read Kantipur as
well as Gorkhapatra, 20 read Kantipur as well as Himalayan times, 15 read
Gorkhapatra as well as Himalayan times and 5 read all three news papers.
a.
Draw
the Venn-diagram to illustrate the above information.
b.
How
many people don't read all three news papers.
22. In a survey of a group of students it
was found that 60 like to listen poems,
45 liked to listen stories, 35 liked to listen both and 10 did not like to
listen both. Then
a.
Present
the above information in a Venn-diagram.
b.
How
many students were surveyed?
c.
How
many students were liked to listen the story only?
23. In a survey of a group showed that 60
liked tea, 45 liked coffee, 30 liked milk, 25 liked coffee as well as tea. 20
liked tea as well as milk, 15 liked Coffee as well as milk and 10 liked all
three how many were asked this question. Solve by drawing venn -diagram.
24. Among the candidates appeared in an
examination, 80% passed in English, 85% in Maths and 75% in both English and
Maths. Find the total number of candidates if 45 candidates were failed in both
English and Maths.
25. By filling the following information in
a venn diagram, Find the cardinal number of n (U). n(L) = 14, n(M) = 13, n(N) =
22, n(LÇMÇN) = 6, n(LÇM) = 7, n(MÇN) = 9, n(LÇN) = 11, n(
) = 4
) = 4
26. In a school 60 students passed in
Mathematics, 45 passed in Science and 30 passed in both subjects.
a.
How
many students were there in the school?
b.
How
many students have passed in Mathematics only?
c.
How
many students had passed in Science only?
d.
Represent
the above information in a Venn-diagram
27. In a college, 65 are studying in
mathematics, 50 students are studying in science and 35 students are studying
in both subjects.
a.
How
many students are studying in the college?
b.
How
many students are studying in Mathematics only?
c.
How
many students are studying in Science only?
d.
Represent
the above information in a Venn - diagram.
28. In an examination, it was found that
55% failed in Maths and 45% failed English. If there were 35% passed in both
subjects.
a.
What
percent failed in Maths only?
b.
What
percent failed in English only?
c.
Represent
the above information in a venn diagram.
29. In a survey of a village, it was found
that 85% of the people like Dashain Festival and 60% like Tihar Festival. If
there were 5% people who did not like both festival:
a.
What
percent liked Dashain Festival only?
b.
What
percent liked Tihar Festival only?
c.
Represent
the above information in a Venn-diagram.
30. In a school, all students play either
volleyball or football or both. 300 play football. 250 volleyball and 110 play
both game draw a Venn diagram to find.
a.
Number
of students who play football only.
b.
Number
of students who play volleyball only.
c.
The
total number of students in the school.
31. In a survey of a community of 240
people, it was found that 151 people could speak Newari language, 95 could
speak English language and 14 could speak neither of the languages. Represent
the above information in a Venn-diagram supposing x as the number of people who
can speak both languages.
a.
Find
the value of x.
b.
Find
the number of people who can speak English only.
32. 40% of the students of a school play
football, 30% play volleyball and 20% play both. If 90 students play neither
football nor volleyball use Venn-diagram and find the number of students in the
school. Also find the number of students who play only football.
33. Out of 20 staffs in an office, 15 can
speak local Newari language other than Nepali language, 8 can speak Bhojpuri,
while 3 can not speak any local languages. By drawing venn diagram, find the
number of staffs.
a.
Who
can speak at least any one local language?
b.
Who
can speak any one local language only out at the two.
34. 40 students were asked what they would
like milk or curd. 30 said they would like curd, 25 said they would like milk
and 5 said they would neither like milk nor curd. By drawing Venn diagram, find
the number of students.
a.
Who
like milk only?
b.
Who
like curd only?
c.
Who
like either milk or curd, any one only?
35. Set P & Q are two subsets of a
universal set U. Illustrate the given information in a venn -diagram &
solve the following problems.If n(U) = 40, n(P) = 25, n(Q) = 18, n(PÇQ) = 5 n(PÈQ) = ? n(
) = ?, n(P - Q) = ? n(Q-P) = ?
) = ?, n(P - Q) = ? n(Q-P) = ?
36. If U = {X:X is a positive integer less
than 16} A = {Y:Y is a prime number} B =
{Z:Z is an odd number} then write down the cardinal value by drawing venn
diagram.
a. n(AÇB)
b. n(
)
)
c. n(A - B)
d. n[U-(AÇB)]
37. By asking question in a group, 110
answered TB spread through drugs, 75 said through smoking and 60 said through
food. Among them, 25 said from both drugs and smoking, 10 said from smoking
& food & 10 said from drug and food, while 5 said from all three.
a.
How
many pedestrians were involved? Solve by drawing Venn-diagram.
b.
How
many said TB spreads through drugs only?
38. In a group 30 students read Math, 24
read Economic, 22 read Statistics 14 read Math only,8 read Economics only, 6
read Math and Statistics only, 2 read Math and Economics only and 8 read
neither of them
a.
Find
the number of students in their group?
b.
How
many students read Economics and Statistics only?
c.
How
many students read all three subjects?
d.
Show
all the information in Venn-diagram.
39. In a class of 25 students, 12 have
taken Mathematics, 8 have taken Mathematics but not Biology. Find the number of
students who have taken Mathematics and Biology and those who have taken
Biology but not Mathematics. Solve by making a Venn-diagram.
40. In a interview of 50 people. 15 liked
milk but not coffee, 5 liked coffee and milk and 5 did not like both. How many
liked coffee only? Represent all result in venn diagram also.
41. Each of a group of 20 students study at
least one of the three subjects Nepali, English and Maths. All those who study
English also study Nepali 3 study all three subjects. 4 students only study
Nepali. 8 students study English. 14 students study Nepali. Draw Venn-diagram
to illustrate above information.
a.
How
many students study only Nepali and Maths but not English?
b.
How
many students study only Maths?
c.
Show
all the information in Venn diagram?
42. Each group of 25 students studies at
least one of the three subjects Nepali, English and Maths. All those who study
English also study Nepali, 4 students study all three subjects, 5 students
study only Nepali. 7 students study English and 15 students study Nepali.
a.
Draw
the venn-diagram to illustrate above information.
b. How many students study Nepali and Math
but not a English?
c. How many students study math only?
43. In a group of students 18 read Account,
19 read Maths, 16 read Science. 6 read Account only, 9 read Maths only, 5 read
Maths and Account only, 2 read Maths and Science only. By using venn-diagram,
find the following
a. How many read all subjects?
b. How many read science only?
c. How many read account and science?
d. How many students are there altogether?
44. Out of 50 students in a class like
Mathematics or Science or both. Among them 20 like both subjects and the ratio
of Maths and Science is 3:2
a. Find the number of students who like
Maths only.
b. Find the number of students who like
Science only.
c. Illustrate the above information in a
venn diagram.
45. In a class of 75 students, 30 students
liked Nepali but not Science and 25 students liked Science but not Neplai. If
10 students did not like both, how many students liked both subjects and
represent the above information in venn-diagram.
46. In a class of 55 students, 15 students
liked maths but not English and 18 students liked English but not Math. If 5
students did not like both, how many students liked both subjects and represent
the above information in Venn-diagram.
47. In an election 1400 voters did not cast
their votes and 400 votes are declared invalid. Two candidates A and B in the
election A defected B by 60 votes. It was found that A secured 2400 of total
rolled votes. Find the number of voters.
48. In a survey among 100 people, 50 liked
coffee, 30 liked milk, 40 liked tea, 20 like coffee only, 25 liked tea only, 10
liked tea and coffee and 5 liked tea, coffee and milk all. Using venn-diagram,
find the number of people who liked neither of these.
49. An
ice-cream shop sold three type of ice creams A, B & C out of the customers
questioned, 470 liked A, 300 liked B, 350 liked C, 130 liked A and B, 120 liked
A and C, 70 liked B and C, 50 liked all three.
a. Draw the venn-diagram to illustrate
above information
b. How many liked exactly two types?
50. A survey was done about mobile and
telephone facility 200 people had telephone facility, 25 had both facility 135
people did not have telephone facility and 300 did not have mobile facility?
a. How many participants in the survey?
b. How many had mobile facility only?
51. In a class of 65 students, 10 students
liked Maths but not English and 20 students liked English but not Maths. If 5
students did not like both how many students liked both subjects? Solve by
Venn-diagram.
52. In a result of first terminal
examination of class ten 20% students are passed in all three subjects 46%
failed in Maths, 57% failed in English, 42% failed in dance, 35% failed in Maths
and English, 25% failed in English and dance, 15% failed in dance and Maths.
a. Draw venn diagram to show above
information
b. Find how many percent failed in all
three subjects
53. In a village of 140 house, 60 believe
in Buddhism, 70 in Hindu Religion and 45 in other religion. Among then 17 house
don't find any difference in Hindu and Buddhims, 18 house don't find any
different in Hindu and other religion while 16 houses don't find any difference
between Buddhism and other religion. If 6 houses don't believe in any religion,
find how many houses do not find any difference in any religion. Show it in
venn-diagram.
54. In a group of players 40 play
Volleyball out of which 25 play volleyball only. 10 play football only and 8
play badminton only 27 play football, 30 play badminton out of which 15 play
volleyball and badminton both. Using venn-diagram find.
a. How many play all three games?
b. How many play two games only?
55. In an interview of 60 people space
times, Rajdhani and Himalayan times are liked by 45, 30 and 15 people
respectively. If the total number of people who liked only two magazines in 22
and they liked at least one of the magazines. Find the number of people who
liked all the magazines.
56. In an examination 48% failed in
science, 39% in account and 33% in History, 12% in science and Account, 9% in
science and History and 13% in Account and History and 3% in all three
subjects. Draw Venn-diagram to represent the given information and find the.
a. Percentage passed in all three
subjects.
b. Percentage failed exactly in two
subjects.
c.
Percentage
failed exactly in one subject.
Answers
1. 75
2. 70
3. 25, 40
4. 35%, 25%
5. 13
6. 68
7. 11
8. 250, 1400
9. 125, 625
10. 40, 10, 20
11. 41, 31, 14
12. 15
13. 10
14. 3
15. 15
16. 2000
17. 100
18. 5%
19. 5%
20. 15
21. 5
22. 80, 10
23. 85
24. 450
25. 32
26. 75, 30, 15
27. 80, 30, 15
28. 20%, 10%
29. 35%, 10%
30. 190, 140, 440
31. 20, 75
32. 180, 36
33. 17, 11
34. 5, 10, 15
35. 38, 2, 20, 13
36. 5, 6, 1, 10
37. 205, 80
38. 54, 6, 8
39. 4, 13
40. 25
41. 2, 6
42. 3,10
43. 3, 7, 7, 36
44. 22, 8
45. 10
46. 17
47. 6540
48. 20
49. 170
50. 335, 10
51. 30
52. 10%
53. 10
54. 10, 12
55. 4
56. 11%, 25%, 61%
------------------------------------------------------------------------------------------------------------------------------
1.
Ram
can do a work in 9 days and Shyam can do it in 12 days. In how many days, both
together, can do the work?
2.
A
and B can do a work in 30 days and 40 days respectively. In how many days can A
and B working together do it?
3.
A
and B can do a work in 12 days, which A alone can do in 30 days, In how many
days B alone can do it ?
4. A and B can do a piece of work in 12
days. B alone can do it in 30 days. Both started the work together but B leaves
after 5 days. In how many days is the whole work completed?
5.
Mohan
and Sohan can do a piece of work in 12 days. Mohan alone can do it in 18 days.
Both started the work together, but Mohan left the work after 6 days. How long
will Sohan work alone to finish the remaining work?
6.
A
and B can finish a piece of work in 12 and 18 days respectively. After some
days when both start to work together A leaves and B completes the remaining
work in6 days. How many days has A worked together before he left?
7.
A,
B and C working together can do a piece of work in 18 days. A could do it alone
in 72 days. After working together for 6 days. A is fallen ill. How long will B
and C together take to finish the remaining work?
8.
A,
B, and C can finish a piece of work in 30, 40 and 60 days respectively 10 days
after they started to work together B leaves. 4 days after B left, A leaves and
C completes the remaining work. Find how many days C had worked altogether.
9.
A
and B can do a piece of work in 45 and 30 days respectively. They work at it together
for some days then A leaves 5 days before completion the work. How many days
would they work together?
10. A can do a piece of work in 20 days, B
can do it in 30 days and C in 40 days. Three of them started the work together.
A left the work after 5 days and C left it in 10 days before its completion.
Find in how many days the work might have been finished.
11. A, B and C can do a piece of work in 15
days, 20 days and 30 days respectively. Three of them started the work together
but A left after 5 days and B left 2 days before its completion. Find in how
many days the work might have been finished.
12. A can do a piece of work in 10 days, B
can do it in 20 days and C in 30 days Three of them started the work together.
A left the work after 4 days and C left it some days before its completion. If the
work is completed in 9days, for how many days did C work?
13. X, Y and Z can finish a piece of work
in 20, 30 and 40 days respectively. If x left the work after working for 5
days, in how many days can Y and Z together complete the remaining work?
14. If 12 labours can do a piece of work in
15 days working 8 hours a day, how many days will 10 labours take to finish
half of it working 9 hours a day?
15. 20 men can do a piece of work in 24
days. After working for few days, 4 men are added and the work was finished 3
days earlier. After how many days were 4 men added?
16. A piece of work was to be completed in
40 days. Then 10 more men were employed and they finished of work in 20 days, then 10 more men
added and work was completed in time, find the number of men employed the
first.
17. 20 men can finish a piece of work in 30
days. When should 5 men leave the work, so that if may be finished 35 days?
18. 40 men can do a piece of work in 24
days. After working for a few days 8 men are added and the whole work as
completed 3 days earlier. After how many days were those 8 men added?
19. 6 labours can finish a work in 120 days
working 7 hours daily. If the work is to be finished in 105 days by working 6
hours daily, how labours will be required?
20. A contractor undertakes to dig a canal
12 km. long in 350 days and employs 45 men. He finds that after 200 days of
working only 4 kilometers of canal have been completed. How many extra men must
be employed to finish the work in time?
21. A certain number of men can complete a
piece of work in 90 days. If, however, there are 15 men less, it will take 10
days more for the work to complete. How many men were there originally?
22. 12 men are engaged to do a piece of
work in 15 days. After working for 6 days they found that only of the work is done. How many men
should be added to finish the work in time?
23. 200 labours need 50 days to construct a
road of 4 km. long working 8 hours a day. How many labours should be decreased
to construct the same road in 80 days working 10 hours a day?
24. 55 men can finish a piece of work in 42
days. How many additional men must be added to complete the work 9 work 9 days
earlier?
25. 16 men are engaged to do a piece of
work in 20 days. After 8 days it is found that only of the work is done. How many
additional men should be taken to complete the work in time.
26. A men undertakes to do a certain job in
32 days. He hires 12 men for the job At the end of 8 days, only one fifth of
the work was completed. How many extra men must be employed in order to
complete the work in time?
27. A contractor had to finish a work in 30
days and he employed some men to do the work. They finished half of the work in
20 days. When 60 more men were added the work was finished on the specified
time. How many men were employed in the beginning?
28. A piece of work was to be completed in
30 days. A number of men employed upon it did only half the work in 18 days. 12
more men were added and the work was completed in the specified time. How many
men were employed at first?
29. A contractor had to finish a work in 60
days and he employed 60 laboures to do the work. They finished half of the work
in 40 days. How many more labourers should be added to finish the work in
specified time?
30. 20 men can do a piece of work in 24
days. After working for 6 days, an additional number of men are taken to finish
the work in 21 days from the beginning. Find the number of additional men.
31. A piece of work has to be completed in
30 days. A number of men employed
in it and did only half of the work in 20 days. 20 more men were added and work was completed in the
specific time. How many men
were employed first?
32. A piece of work had to be completed in
60 days. A number of men employed upon it and they did only of the work in 40 days. 20 more men
were added and the work was completed in the specified days. How many men were
employed at first?
33. A contractor undertook to do a work in
40 days and employed a certain number of men upon it who did only half of the
work in 24 days. So, 16 more men added to do the work in time. How many men
were employed initially?
34. A work was to be finished in 16 days
and for this 30 persons started together But only work in finished after 10 days. Find
the number of additional men should betaken to do the work in given time.
35. 20 men can do a work in 30 days; after
how long time should 5 men leave so that the work may be completed in 35 days?
36. 4 men can do a work in 5 days. But due
to Nepal-Band, no work is done on the third day. How many extra men should be
added to complete the work in the fixed schedule?
37. A piece of work was to be completed in
30 days, A number of man employed on it, did only half of the work in 20 days,
Again 20 more men were added and the work was completed in specified time. How
many were employed at first?
- If
10 pumps draw 430 liters of water is 10 minutes, how many liters will be
drawn by 6 pumps in 20 minutes?
39. A tap can fill a cistern in 10 minutes
while other can empty in 15 minutes. The cistern being empty and if both the
taps are opened together, in how many minutes will the cistern be full?
40. Two taps A and B fill a tank in 8 hours
and 10 hours respectively when they are opened separately. If both the taps are
opened at the same time, how long will it take to fill the tank?
41. Three taps can fill a cistern in 36
minutes, 30 minutes and 20 minutes respectively. The cistern being empty all
the three taps are kept open and after 6 minutes the first tap is closed. In
how many more minutes will the cistern be full?
42. Two pipes A and B can fill a tank in 24
min and 32 min. respectively. If both pipes are opened simultaneously, after
how much time B should be closed so that the tank is full in 18 minutes?
43. A and B can fill a casern in 20 min.
and 25 min. respectively. Both the pipes are kept open for 5 min. and then the
second pipe is turned off. In how many minutes more is the tank completely
filled?
44. A and B can fill a tank in 2 hrs. and 4
hrs respectively. Both were opened at once but after sometime the first was
shut up and the tank was filled in 2 hrs more. When did the first pipe A shut
up?
45. Two pipes A and B can fill a tank in 36
min. and 45 min. respectively. A waste pipe C cans empty the tank in 30 min.
First A and B are opened. After 7 min, C is also opened. In how much time, the
tank is full?
46. A cistern has a leak which would empty
it in 8 hours. A tap is turned on which admits 6 liters a minute into the
cistern and it is now emptied in 12 hours. How many liters does the cistern
hold?
47. A and B can fill a cistern in 60 min,
and 75 min. respectively. If all the pipes (including a waste -pipe C) are
opened together, the cistern is full in 50 minutes. Find the time required for
C to empty the full cistern.
48. Surav takes one day to do a work;
Gaurav takes two days to do the same work. IF Gaurav takes 24 days to do 2/5 of
the work, in how many days will both together finish the whole work?
49. Ram can do twice as much work as Shyam.
If they together can complete a work in 24 days. In how many days will each
take to complete the work?
50. A takes twice as much time as B and
thrice as much time as C to finish a piece of work. If they work together they
can finish the work in 4 days. Find the time each will take to finish the work?
51. A alone can do a certain work in the
same time in which B and C together can do it. If A and B could together do it
in 10 days and C alone in 50 days, in what time can B alone do it?
52. A is thrice as good a workman as B and
is therefore able to finish a piece of work in 60 days less than B. Find the
time in which they can do it working together.
53. A can do as much work in 2 days as B
can do in 3 days and B can do as much work in 4 days as C in 5 days. It takes
20 takes 20 days to complete the work if all of them work together. How long
would B take to do all the work by himself?
54. A takes twice as much time as B and
thrice as much time as C to finish a piece of work. If they work together they
can finish the whole work in 5 days. Find the time each will take to finish the
work separately.
55. Promod and Ramchandra can do a pieces
can do a piece of work in 30 and 20 days respectively After they work together
for some days, Ramchandra left. If promod completes the remaining worked in 15
days how long had Ramchandra worked together.
56. A can do a work in 30 days and B in 40
days. They start working together but after 8 days B leaves. In how many days A
can finish the remaining work?
57. Mohan and Sohan together can finish a
piece of work in 30 days. After they worked for 20 days. Sohan left. If Mohan
can finish the remaining work in 35 days, How long Sohan alone can finish the
whole work?
58. Ram and Shyam can do a piece of work in
20 days and 25 days respectively. They work to together of 5 days and Shyam
left the work. In how many days will Ram finish the remaining work?
59. A and B can do a piece of work in 24
days. A takes 40 days to complete the same work. After they work for 8 days, A
leaves, If B completes the remaining work, in how many days was the whole work
completed?
60. A can do a piece of work in 14 days. B
can do the same work in 21 days. After they work for 7 days, A leaves. If B
completes the remaining work; in how many days was the whole work completed?
61. Ram and Shyam together can finish a
piece of work in 8 days. Ram alone can finish the work in 12 days. If he leaves
after working for 4 days alone. In how many days will Shyam finish the
remaining work alone?
62. A can do a piece of work in 18 days and
B in 24 days. They both worked together and after some days A left. If B
finished the remaining work in 3 days, how long did A work together?
63. A can do a piece of work in 36 days and
B in 54 days. They both worked together and after some days B left. If A
finished the remaining work in 11 days, how long did B work together?
64. C and D can finish a piece of work in
20 days. After they work for 12 days D left. If C alone can finish teh
remaining work in 40 days, how long would D alone take to do whole work?
65. A and B can finish a piece of work in
40 days. After they worked for 25 days. B left. If A can finish the remaining
work in 45 days. How long B alone can finish the whole work?
66. A and B can do a work in 12 days, B and
C in 15 days C and A in 20 days. In how many days will they finish it together?
67. A can do a work in 20 days and B in 12
days. B worked for 9 days and left. In what time will A complete the remaining
work?
68. A and B can do a work in 24 and 16 days
respectively. With the help of C, they can
finish it in 8days, Find in what time will A and C together do it?
69. Aviral and Abhiyan can do a work in 25
and 20 days respectively. Aviral started the work and was joined by Abhiyan after
10 days. How long was the work last for?
70. 12 men can dig a field in 8 days. Three
days after they started to work together, 3 extra men joined them, Find the
time taken by all of them to complete the remaining work.
71. A and B can together do a piece of work
in 30 days. They worked for it for 20 days and then B left. The remaining work
was done by A alone in 20 more days. Find the time required for A to do the
whole work alone.
72. A and B can do a work in 45 and 40 days
respectively. They started the work together, but A leaves after some days and
B finished the remaining work in 23 days. After how long time did A leave?
73. A and B can do a work in 20 and 30 days
respectively. They start to work together but A leaves 5 days before the
completion. In how many days to do the whole work?
74. A and B can do a work in 72 days. If A
works alone for the last 20 days, it is completed in 80 days. How many days
will be required for B to do the whole work alone?
75. To do a work A would take twice as long
as B and C together. B takes 3 times as along as C and A together. All of them
together can do it in 12 days. Find in what time A, B and C alone can do it?
76. A can do as much work in 2 days as B in
3 days and B can do as much work in 4 days as C in 5 days. If all of them can
do a work in 20 days, how long would each take to do the work separately?
77. While A does of a work. B does and
while B does, C does .In how many hours will C finish a work
which can be finished by A in 20 hours?
78. A, B and C can do a work in 20, 30 and
40 days respectively. All of them worked together but A left after 5 days and C
left in 10 days before its completion. In how many days required doing the
whole work?
79. A, B and C can do work in 10, 20 and 30
days, A left. C left it some days before completion. If total time taken for
the whole work is days. For how many days did C work?
80. A, B and C can do a work 50, 70 and 90
days respectively. Only A started the work and B joined after 10 days, C joined
after 5 days from this and all of them continued till it was over. In how many
total days taken for the whole work.
81. A, B and C can do a work in 60, 80 and
100 days respectively. A and B started the work. After 10 days A left but C
joined. After 20 days from the join of C, B left but A rejoined. In how many
total days to do the whole work?
82. A, B and C together can do a work in 6 days,
which B alone can do in 16 days and B and C together in 10 days In how many
days can A and B together do it?
83. A and B can do a work in 10 days, B and
C in 15 days, A and C in 25 days. They all work at it together for 4 days, A
then leaves and B and C go on together for 5 days more and then B leaves, how
many more days will C complete the work?
84. A can do work in 20 days, A and B
together in days. A works alone for 8 days, A and C
together for 6 days, and B finishes it in 3 days. Find in what time B and C
together could do it?
85. A can do a work in 8 days, which B can
destroy in 3 days, A has worked 6 days, during the last 2 of which B has been
destroyed. How many days must A now work alone in order to complete his task?
86. A and B can do a work in 8 days and 7
days respectively. They work alternately for a day. If A starts the work, find
in how many total days completed to do work?
87. 25 men are employed to do a work which
they could finish it in 20 days but there is a drop off by 5 men at the end of
every 10 days. In what time will the work be completed?
88. A cistern would be filled by a tap A in
3 hours, or emptied by a tap B in 3 hours. The
cistern being half full A is turned on at 8:00 Am and B at 8:45 Am Find when
the cistern will again be half full?
89. A is twice and B is just as good a
workman as C. The three work together for two days, and then A works alone for
half a day and B for a day. How long would it have taken A and C together to
complete as much as the three will have thus performed?
Answers
1. 5days
2. 17days
3. 20 days
4.
5. 18 days
6. 4days
7. 16 days
8. 17 days
9. 15 days
10. 17days
11. 9days l
12. 4days
13. 7days
14. 8 days
15. 6 days
16. 15 days
17. 15 days
18. 6 days
19. 8
20. 75
21. 150
22. 4
23. 100
24. 15
25. 16
26. 4
27. 60
28. 24
29. 60
30. 4
31. 20
32. 20
33. 32
34. 10
35. 15 days
36. 2
37. 32
38. 516 l.
39. 30 min.
40. 4hrs.
41. 4 min.
42. 8 min
43. 11 min.
44. After 40 min.
45. 46 min
46. 2880 lit.
47. 100min.
48. 20 days
49. 36 days, 72 days
50. 24 days, 12 days, 8
days
51. 25 days
52. 22days
53. 66 days
54. 30 days, 15 days, 10 days
55. 6 days
56. 16 days
57. 42 days
58. 11 days
59. 48 days
60. 10days
61. 16 days
62. 9 days
63. 15 days
64. 25 days
65. 60 days
66. 10 days
67. 5 days
68. 16 days
69. 16days
70. 4 days
71. 60 days
72. After 9 days
73. 15 days
74. 180 days
75. 36 days, 48 days, 28days
76. 44 days, 66 days, 82days
77. 32 hours.
78. 17 days
79. 4days
80. 28 days
81. 39days
82. 7days
83. 76 days
84. 14days
85. 7days
86. 7 days
87. 23days
88. 1:15 pm
89. 3days
The questions are too nice
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ReplyDeleteplz share some question from opt math for slc thanx
ReplyDeletePut unseen theorems from geometry
ReplyDeleteit is great but also keep some chalanges questions too.
ReplyDeletePlz solve set question 55
ReplyDeleteQuestion 6
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