வெல்லுங்கள் CSAT 2025 - 11: Q and A on Time & Work

Questions & Answers - (Multiple Choice) - TIME & WORK
கொள்குறி வினா- விடைகள் - காலமும் வேலையும்

1. A similar work is allotted to four persons A, B, C and D separately. A can do one-third of the work in 12 days whereas B can do 40% of the work in 15 days. C can do 60% of the work in 21 days and D finishes three-fourths of the work in 25 days. On a particular day all of them started to do the work. Find who will finish the work at the last.
a. A b. B
c. C d. D

2. A and B got a job to do. They together finished 40% of the work after the start of 6 days. B left the job and A alone finished the remaining work in 18 days. In how many days B alone can complete the whole job?
a. 20 b. 24
c. 30 d. 32

3. A, B and C alone can do a piece of a work in 3 days, 6 days and 9 days respectively. A alone starts the work on Sunday. B alone works on Monday, C alone works on Tuesday. Again A alone works on Wednesday, B on Thursday and C on Friday and so on. On which day the work will be completed?
a. Sunday b. Saturday
c. Friday d. Thursday

4. A group of men decided to do a job in 6 days. But since 6 men dropped out every day, the job got completed at the end of the 9th day. How many men were
there at the beginning?
a. 72 b. 96
c. 108 d. 216

5. One man can do as much work in one day as a woman can do in 2 days. A child does one-sixth the work in a day as a man. If a contractor hires 26 pairs of hands—men, women and children in the ratio 5 : 6 : 2 and pays them in all
₹ 7500 at the end of the day’ s work, what must the daily wages of a woman be, if the wages are proportional to the amount of work done ?
a. ₹300 b. ₹ 225
c. ₹200 d. ₹ 75

6. P is thrice as good as workman as Q and hence is able to finish a work in 30 days less than Q. The number of days to be taken if both work together is
a. 12 b. 16
c. 11.25 d. 22.5

7. X can do a work in the same time Y and Z together can do it. If Z alone can do it in 25 days and both X and Y could together do it in 5 days, then the number of days Y alone can do the same work is
a. 25 b. 15
c. 14 d. 12.5

8. A, B and C can complete a work in 3, 6 and 2 days respectively. In how many days all three together complete the same work?
a. 1 b. 1.5
c. 1.6 d. 0.8

9. Sneha and Mary are working on an assignment. Mary takes 6 hours to type 30 pages whereas Sneha takes 5 hours to type 40 pages. How long will they take working together on two different Laptops to type an assignment of 104 pages?
a. 7hrs b. 8hrs
c. 10hrs d. 9hrs

10. A, B and C can complete a work in 9, 12 and 24 days respectively. A and B started the work but they forced to leave after 3 days. In how many days the balance work was done by C ?
a. 6 b. 8
c. 10 d. 12

11. A machine A can print 10000 books in 3 hours, machine B can print the same number of books in 6 hours whereas machine C can print in 18 hours. All machines started at 10.00a.m while C is closed at 11.00a.m and the remaining two machines complete work. At what time will to print 10000 books be finished?
a. 11.30 a.m b. 12 noon
c. 11.50 a.m d. 11.40 a.m.

12. A does half as much work as B and C. C does half as much work as A and B together. If C alone can do the work in 30 days, then the number of days that all of them together finish the work is
a. 16 b. 8
c. 10 d. 12

13. A wheel rotates 12 times per minute and moves 24 cm during each rotation. How many metres does the wheel move in 3 hours?
a. 518.4 b. 815.4
c. 185.4 d. 581.4

14. 32 persons can dig a trench 50m long, 2m wide and 2m deep in 12days 10hours daily. In how many days working 8 hours daily by 80 persons dig another trench 75m long, 2m wide and 4m deep?
a. 12 b. 18
c. 24 d. 30

15. The ratio between the rates of working of A and B is 3 : 5 . If the time taken to do a work by B is 10 days less than A, then the number of days that both together do the same work is
a. 8.75 b. 10
c. 11.625 d. 9.375

Answers

1. b 2. c 3. d 4. a 5. b

6. c 7. d 8. a 9. b 10. c

11.d 12. c 13. a 14. b 15. d

1. A can do the work in 12×3
= 36 days
B can do the work in 15×(100/40)
= 37.5 days
C can do the work in 21×(100/60)
= 35 days
D can do the work in 25×(4/3)
= 33.3 days
D finishes first
B finishes at the last.

2. A alone do 60% in 18 days.
A alone can do the whole job in 18×(100/60) = 30 days
The part of the job done by both A and B in 6 days = 40/100 = 2/5
The part of the job done by A in 6 days is 6/30 = 1/5
The part of the job done by B in 6 days is 2/5 - 1/5 = 1/5
The part of the job done by B in 1 day
=1/30
Hence B alone can do the whole job in
30 days

3. The parts of the work done by A, B and C are 1/3, 1/6 and 1/9 respectively.
The part of the work done in first 3 days
= 1/3 + 1/6 + 1/9 = 11/18
After 4th day end, the remaining part of the work = 1 - (11/18) - 1/3 = 1/18.
On fifth day B finishes the work.
i.e., on subsequent Thursday, the whole work will be completed.

4. Let the number of men were
there at the beginning be 'm'.
Mandays requirement = 6m Mandays
By problem
6m = m + (m-6) + (m-12) + (m-18) + ......... (m-48) = 9m - 216
-> 3m = 216 -> m = 72.

5. Ratio of number of men, women and children = 5 : 6 : 2 and the total number of men, women and children = 26.
Therefore the number of men = 10, women = 12 and children = 4.

Ratio of work done by
man : woman : child = 1 : 1/2 : 1/6
= 6 : 3 : 1

∴ Ratio of work done by 10 men, 12 women and 4 children

= (10 × 6) : (12 × 3) : (4 × 1) = 15 : 9 : 1

Hence Rs.7500 would be divided in this ratio 15 : 9 : 1

That makes ₹4500 for men, ₹ 2700 for women and ₹300 for children. Hence 12 women earn Rs2700 in a day. So the daily wage of a woman is equal to 2700/12 = ₹225

6. The ratio of number of days taken by P and Q is 1 : 3
If difference is 2, the number of days taken by Q to complete the work is
30/(2/3) = 45 days
So, P can take only 15 days
P and Q together to do the work is
(15×45)/(15+45) = 45/4 = 11.25 days.

7. (X + Y)'s 1 day's work = 1/5.
Z's 1 day's work = 1/25.
(X + Y + Z)'s 1 day's work
= 1/5 + 1/25 = 6/25
since
X's 1 day's work =(Y + Z)'s 1 day's work
-> 2×(X's 1 day's work) = 6/25
-> (X's 1 day's work) = 3/25
(Y's 1 day's work) = 1/5 - 3/25 = 2/25
Hence Y alone can do the work in
25/2 = 12.5 days.

8. One day's work of all A, B and C together is = 1/3 + 1/6 + 1/2
= (2+1+3)/6 = 1
So all three together complete the same work in one day.

9. Number of pages typed by Mary in
one hour = 30/6 = 5
Number of pages typed by Sneha in
one hour = 40/5 = 8
Number of pages typed by both in
one hour = 8 + 5 = 13.
Time taken by both to type 104 pages
= 104/13 = 8 hours.

10.(A+B)'s one day's work
= 1/9 + 1/12 = 7/36
(A+B)'s three days' work = 7/12
Balance part of the work = 1 - 7/12
= 5/12
This 5/12 part of the work done by C
in = 24×(5/12) = 10 days.

11. (A+B+C)'s one hour's work
= 1/3 + 1/6 + 1/18 = 10/18 = 2/3
At the end of 11.00a.m, remaining part of the work = 1 - 2/3 = 1/3.

So, 1/3 work is done by A and B in
(1/3)/{(1/3)+(1/6)} = 2/3 hour = 40mts.
Hence the work will be finished 40 mts after 11.00a.m.
i.e. at 11.40a.m

12. Let one day's work of A, B and C be a, b and c respectively.
Given a =(1/2)(b+c) -> 2a = b + c
-> 3a = a + b + c
Similarly c =(1/2)(a+b) -> 2c = a + b
-> 3c = a + b + c
So 3a = 3c -> a = c
But c = 1/30
But 3c = a + b + c = 3/30 = 1/10
Hence A, B and C together can do the work in 10 days.

13. The number of rotation in 3 hours
= 12 × 60 × 3 = 2160
The total distance covered by the wheel in 3 hours = 2160 × 24 = 51840cm
So in metres = 518.4 m

14. Volume of work done by 32 persons working 10hours per day for 12 days
= 50 × 2 × 2 cu.m.
The number of man hours needed for one cubic metre
= (32×10×12)/(50×2×2) = 19.2
The number of man hours needed for
75 × 2 × 4 cu.m = 19.2 ×75 × 2 × 4
The number of days required for 80 persons working 8 hours per day to dig the trench = (19.2×75×2×4)/(80×8) = 18

15. The ratio of number of days that individually A and B can do the work is
5 : 3.
So the number of days to do the work by A alone is (5)/(5-3) × 10 = 25 days
And the number of days to do the work by B alone is (3)/(5-3) × 10 = 15 days

The number of days that both A and B together do the same work is
(25×15)/(25+15) = 75/8 = 9.375

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