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# Maths : Time & Work (Solved in Steps)

1. Praveen is able to do a piece of work in 15 days and Qureshi can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?

A. 8/15 B. 7/15
C. 11/15 D. 2/11

Explanation :

Amount of work Praveen can do in 1 day = 1/15
Amount of work Qureshi can do in 1 day = 1/20
Amount of work Praveen and Qureshi can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work Praveen and Qureshi can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15

2. Anil can lay railway track between two stations in 16 days. Subin can do the same job in 12 days. With the help of Jyothi, they complete the job in 4 days. How many days does it take for Jyothi alone to complete the work?

A. 9(3/5) days B. 9(1/5) days C. 9(2/5) days D. 10 days

Explanation :

Amount of work anil can do in 1 day = 1/16
Amount of work Subin can do in 1 day = 1/12
Amount of work anil, subin and Jyothi can together do in 1 day = 1/4
Amount of work Jyothi can do in 1 day = 1/4 – (1/16 + 1/ 12) = 3/16 – 1/12 = 5/48
=> Hence Jyothii can do the job on 48/5 days = 9 (3/5) days

3. P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?

A. 10 days B. 14 days C. 15 days D. 9 days

Explanation: Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 × 1/5 = 1 Ie, the work will be done in 15 days

4. Ajeesh is thrice as good as Binu in work. Ajeesh is able to finish a job in 60 days less than Binu. They can finish the work in – days if they work together?

A. 18 days B. 22 ½ days C. 24 days D. 26 days

Explanation :

If Ajeesh completes a work in 1 day, Binu completes the same work in 3 days
Hence, if the difference is 2 days, Binu can complete the work in 3 days
=> if the difference is 60 days, Binu can complete the work in 90 days
=> Amount of work Binu can do in 1 day= 1/90
Amount of work Ajeesh can do in 1 day = 3 × (1/90) = 1/30
Amount of work Ajeesh and Binu can together do in 1 day
= 1/90 + 1/30 = 4/90 = 2/45
=> Ajeesh and Binu together can do the work in 45/2 days
= 22 ½ days

5. Ajay can do a particular work in 6 days . Bilal can do the same work in 8 days. Ajay and Bilal signed to do it for Rs. 3200. They completed the work in 3 days with the help of Deepu. How much is to be paid to Deepu?

A. Rs. 380 B. Rs. 600 C. Rs. 420 D. Rs. 400

Explanation :

Amount of work Ajay can do in 1 day = 1/6
Amount of work Bilal can do in 1 day = 1/8
Amount of work Ajay + Bilal can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work Ajay + Bilal + Deepu can do = 1/3
Amount of work Deepu can do in 1 day = 1/3 – 7/24 = 1/24
work Ajay can do in 1 day: work Bilal can do in 1 day: work deepu can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to Deepu = 3200 × (1/8) = 400

6. 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in – days.

A. 4 days B. 6 days C. 2 days D. 8 days

Explanation :

Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b
Work done by 6 men and 8 women in 1 day = 1/10
=> 6m + 8b = 1/10
=> 60m + 80b = 1 — (1)
Work done by 26 men and 48 women in 1 day = 1/2
=> 26m + 48b = ½
=> 52m + 96b = 1— (2)
Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200
Work done by 15 men and 20 women in 1 day
= 15/100 + 20/200 =1/4
=> Time taken by 15 men and 20 women in doing the work = 4 days

7. A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in — days.

A. 12 hours B. 6 hours C. 8 hours D. 10 hours

Explanation :

Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12
Work done by B in 1 hour = 7/12 – 1/2 = 1/12 => B alone can complete the work in 12 hour

8. P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. How many days does P alone need to finish the remaining work?

A. 8 B. 5 C. 4 D. 6

Explanation :

Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6

9. P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in

A. 30 days B. 25 days C. 20 days D. 15 days

Explanation :

Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/50
Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day × 2 = 6/50
=> Work done by P in 1 day = 3/50
=> Work done by Q and R in 1 day = 3/50
Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25
So Q alone can do the work in 25 days

10. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?

A. 37 ½ days B. 22 days C. 31 days D. 22 days

Explanation :

Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 — (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 —(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days

11. 3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?

A. 50 B. 40 C. 30 D. 20

Explanation :

Work done by 4 men and 6 women in 1 day = 1/8
Work done by 3 men and 7 women in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does work in 1 day. The above equations can be written as
4m + 6w = 1/8 —(1)
3m + 7w = 1/10 —(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 women can do in a day = 10 × (1/
400) = 1/40 Ie, 10 women can complete the work in 40 days

12. A and B can finish a work 30 days if they work together. They worked together for 20 days and then B left. A finished the remaining work in another 20 days. In how many days A alone can finish the work?

A. 60 B. 50 C. 40 D. 30

Explanation :

Amount of work done by A and B in 1 day = 1/30
Amount of work done by A and B in 20 days = 20 × (1/ 30) = 20/30 = 2/3
Remaining work – 1 – 2/3 = 1/3
A completes 1/3 work in 20 days
Amount of work A can do in 1 day = (1/3)/20 = 1/60
=> A can complete the work in 60 days

13. A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in –days.

A. 5 ⁵⁄₁₁ B. 4 ⁵/₁₁ C. 6 ⁴/₁₁ D. 6 ⁵/₁₁

Explanation :

A can complete the work in 12 days working 8 hours a day
=> Number of hours A can complete the work = 12×8 = 96 hours
=> Work done by A in 1 hour = 1/96
B can complete the work in 8 days working 10 hours a day
=> Number of hours B can complete the work = 8×10 = 80 hours
=> Work done by B in 1 hour = 1/80
Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480
=> A and B can complete the work in 480/11 hours
A and B works 8 hours a day
Hence total days to complete the work with A and B working together
= (480/11) / (8) = 60/11 days = 5 ⁵⁄₁₁ days

14. P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?

A. 9 B. 11 C. 13 D. 15

Explanation :

Work done by P in 1 day = 1/23
Let work done by Q in 1 day = q
q × (130/100) = 1/23
=> q = 100/(23×130) = 10/(23×13)
Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13
=> P and Q together can do the work in 13 days

15. P, Q and R can complete a work in 24, 6 and 12 days respectively. The work will be completed in — days if all of them are working together.

A. 2 B. 3 ³⁄₇ C. 4 ¼ D. 5

Explanation :

Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/6
Work done by R in 1 day = 1/12
Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24
=> Working together, they will complete the work in 24/7 days = 3 ³⁄₇days

16. 10 men can complete a work in 7 days. But 10 women7 need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?

A. 5 B. 6 C. 7 D. 8

Explanation :

Work done by 10 men in 1 day = 1/7
Work done by 1 man in 1 day = (1/7)/10 = 1/70
Work done by 10 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/140
Work done by 5 men and 10 women in 1 day = 5 × (1/ 70) + 10 × (1/140)
= 5/70 + 10/140 = 1/7
=> 5 men and 10 women can complete the work in 7 days

17. Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in —– days.

A.14 B. 16 C. 18 D. 20

Explanation :

Work done by Kamal in 1 day = 1/20
Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16
=> Suresh can complete the work in 16 days

18. P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?

A. 5 days B. 10 days C. 14 days D. 22 days

Explanation :

Work done by P in 1 day = 1/20
Work done by Q in 1 day = 1/12
Work done by P in 4 days = 4 × (1/20) = 1/5
Remaining work = 1 – 1/5 = 4/5
Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15
Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6
Total days = 4 + 6 = 10

19. P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if work together. How much time will Q take to do the work alone?

A. 4 B. 5 C. 6 D. 7

Explanation :

Let P takes x days to complete the work
Then Q takes x/2 days and R takes x/3 days to finish the work
Amount of work P does in 1 day = 1/x
Amount of work Q does in 1 day = 2/x
Amount of work R does in 1 day = 3/x
Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x
= 1/x (1 + 2 + 3) = 6/x
6/x = 2
=> x = 12
=> Q takes 12/2 days = 6 days to complete the work

20. P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in — days.

A. 12 B. 16 C. 20 D. 24

Explanation :

Work done by P in 1 day = 1/15
Work done by Q in 1 day = 1/10
Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6
Work done by P and Q in 2 days = 2 × (1/6) = 1/3
Remaining work = 1 – 1/3 = 2/3
Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days
Total time taken = 2 + 10 = 12 days

21. P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?

A. 10 B. 15 C. 18 D. 22

Explanation :

Let work done by P in 1 day = p,
Work done by Q in 1 day = q,
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20
= 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8
Remaining work = 1 = 5/8 = 3/8
Work done by P in 1 day = Work done by P,Q and R in 1 day – Work done by Q and R in 1 day
= 1/16 – 1/24 = 1/48
Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18

22. P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How man D. 4 days will be needed if P and R together do it?

A. 3 B. 8 C. 12 D.14

Explanation :

Let work done by P in 1 day = p
work done by Q in 1 day =q
Work done by R in 1 day = r
p + q = 1/8 —(1)
q + r= 1/12 —(2)
p+ q+ r = 1/6 —(3)
(3) – (2) => p = 1/6 – 1/12 = 1/12
(3) – (1) => r = 1/6 – 1/8 = 1/24
p + r = 1/12 + 1/24 = 3/24 = 1/8
=> P and R will finish the work in 8 days

23. P works twice as fast as Q. If Q alone can complete a work in 12 days, P and Q can finish the work in — days

A. 1 B. 2 C. 3 D. 4

Explanation :

Work done by Q in 1 day = 1/12
Work done by P in 1 day = 2 × (1/12) = 1/6
Work done by P and Q in 1 day = 1/12 + 1/6 = ¼
=> P and Q can finish the work in 4 days

24. A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is

A. 1:3 B. 4:3 C. 2:3 D. 2:1

Explanation :

Work done by 20 women in 1 day = 1/16
Work done by 1 woman in 1 day = 1/(16×20)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×16)
Ratio of the capacity of a man and woman =1/(15×16) :
1/(16×20) = 1/15 : 1/20
= 1/3 :1/4 = 4:3

25. P can do a work in 24 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in — days.

A. 7 B. 8 C. 9 D. 10

Explanation :

Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3×7/36 = 7/12
Remaining work = 1 – 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/24) = 10

26. P, Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?

A. Rs.40 B. Rs.70 C. Rs.90 D. Rs.100

Explanation :

Amount Earned by P,Q and R in 1 day = 1620/9 = 180 —(1)
Amount Earned by P and R in 1 day = 600/5 = 120 —(2)
Amount Earned by Q and R in 1 day = 910/7 = 130 —(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
– Amount Earned by P,Q and R in 1 day = 120+130-180 = 70
=>Amount Earned by R in 1 day = 70

27. Assume that 20 cows and 40 goats can be kept for 10 days for Rs.460. If the cost of keeping 5 goats is the same as the cost of keeping 1 cow, what will be the cost for keeping 50 cows and 30 goats for 12 days?

A. Rs.1104 B. Rs.1000 C. Rs.934 D. Rs.1210

Explanation :

Assume that cost of keeping a cow for 1 day = c,
cost of keeping a goat for 1 day = g
Cost of keeping 20 cows and 40 goats for 10 days = 460
Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46
=> 20c + 40g = 46
=> 10c + 20g = 23 —(1)
Given that 5g = c
Hence equation (1) can be written as 10c + 4c = 23 =>
14c =23
=> c=23/14
cost of keeping 50 cows and 30 goats for 1 day
= 50c + 30g
= 50c + 6c (substituted 5g = c)
= 56 c = 56×23/14 = 92
Cost of keeping 50 cows and 30 goats for 12 days = 12×92 = 1104

28. There is a group of persons each of whom can complete a piece of work in 16 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many days are needed to complete the work?

A. 3 ¼ days B. 4⅓ days C. 5⅙days D. 6⅕ days

Explanation :

Work completed in 1st day = 1/16
Work completed in 2nd day = (1/16) + (1/16) = 2/16
Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16 …
An easy way to attack such problems is from the choices.
You can see the choices are very close to each other. So just see one by one.
For instance, The first choice given in 3 ¼
The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16
The work done in 4 days = (1+2+3+4)/16 = 10/16
The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn’t it?
The work done in 6 days = (1+2+3+4+5+6)/16 > 1
Hence the answer is less than 6, but greater than 5. Hence