Q: P and Q together can complete a job in 16 days. Q and R together can complete it in 24 days, and R and P together can do it in 32 days. In how many days can P alone complete the job?

38 2/5 days. Let daily work rates be P, Q, and R. Then $P+Q=1/16$, $Q+R=1/24$, and $R+P=1/32$. Adding gives $2(P+Q+R)=1/16+1/24+1/32=13/96$, so $P+Q+R=13/192$. Hence $P=(P+Q+R)-(Q+R)=13/192-1/24=5/192$, so P alone takes $192/5=38\frac{2}{5}$ days.

Q: A traveller goes from City P to Q at 24 km/h in 5 hours. By how much should the speed be increased to complete the journey in 3 hours?

16 km/h. The distance between the cities is $24 \times 5 = 120$ km. To cover 120 km in 3 hours, the required speed is $120/3 = 40$ km/h. So the increase in speed is $40 - 24 = 16$ km/h.

Question 1

P and Q together can complete a job in 16 days. Q and R together can complete it in 24 days, and R and P together can do it in 32 days. In how many days can P alone complete the job?

Accepted Answer

38 2/5 days. Let daily work rates be P, Q, and R. Then $P+Q=1/16$, $Q+R=1/24$, and $R+P=1/32$. Adding gives $2(P+Q+R)=1/16+1/24+1/32=13/96$, so $P+Q+R=13/192$. Hence $P=(P+Q+R)-(Q+R)=13/192-1/24=5/192$, so P alone takes $192/5=38\frac{2}{5}$ days.

Question 2

X can complete a project in 14 days and Y in 10 days. When Z joins them, the work is finished in 3.5 days. How many days would Z need alone?

Accepted Answer

8.75 days. X’s rate is $1/14$ per day and Y’s rate is $1/10$ per day. Together with Z, the rate is $1/3.5=2/7$ per day. So Z’s rate is $2/7 - 1/14 - 1/10 = 2/35$, meaning Z alone takes 35/4 = 8.75 days.

Question 3

P can complete a task in 6 days, and Q can destroy it in 4 days. P works for 3 days, then Q joins for 2 days. In how many days will P finish the remaining work alone?

Accepted Answer

4 days. P’s rate is $1/6$ per day and Q’s rate is $-1/4$ per day. In 3 days P completes $1/2$ work; in the next 2 days, together they do $2(1/6-1/4)=-1/6$ work, so remaining work is $1/2+1/6=2/3$. P alone needs $(2/3)/(1/6)=4$ days.

Question 4

A traveller goes from City P to Q at 24 km/h in 5 hours. By how much should the speed be increased to complete the journey in 3 hours?

Accepted Answer

16 km/h. The distance between the cities is $24 	imes 5 = 120$ km. To cover 120 km in 3 hours, the required speed is $120/3 = 40$ km/h. So the increase in speed is $40 - 24 = 16$ km/h.

Question 5

X can do a job in 10 days, and Y can do it in 15 days. They work together for 4 days. What fraction of the work remains?

Accepted Answer

1/3. X's one-day work is $1/10$ and Y's one-day work is $1/15$. Together they do $1/10 + 1/15 = 1/6$ of the work per day, so in 4 days they complete $4/6 = 2/3$ of the work. Therefore, the remaining work is $1 - 2/3 = 1/3$.

Question 6

X and Y complete a task in 14 days, and Y and Z complete it in 18 days. If X works for 6 days, Y for 8 days, and Z for 12 days to complete the task, how many days will Z alone take approximately?

Accepted Answer

22 days. Let the daily work rates be X, Y, Z. Then X+Y = 1/14 and Y+Z = 1/18. The total work done is 6X + 8Y + 12Z = 1. Solving these equations gives Z ≈ 1/22 of the work per day, so Z alone takes about 22 days.

Question 7

P completes a job in 15 days and Q in 20 days. P and Q agree to do the work for ₹6,000. With R, they finish in 4 days. What is R's payment?

Accepted Answer

₹ 3,200. P's rate is $1/15$ and Q's rate is $1/20$, so together they work at $7/60$ per day. In 4 days, P+Q do $28/60=7/15$ of the work, so R does the remaining $8/15$. Therefore R's payment is $6000	imes \frac{8}{15}=3200$.

Question 8

The ratio of the times taken by X and Y to complete a task is $5:3$. If Y alone takes 15 hours, how long will X and Y together take?

Accepted Answer

9.375 hrs. Since time is inversely proportional to work rate, X:Y time ratio $=5:3$ means X:Y efficiency ratio $=3:5$. If Y takes 15 hours, X takes $15	imes \frac{5}{3}=25$ hours. Together their rate is $1/25+1/15=8/75$, so time taken is $75/8=9.375$ hours.

Question 9

C is four times as efficient a worker as D, and C can complete a work in 45 days less than D. If they work together, in how many days can they finish the work?

Accepted Answer

12 days. If D takes x days, then C, being four times as efficient, takes x/4 days. Given x - x/4 = 45, so x = 60 and C takes 15 days. Together, their rate is 1/15 + 1/60 = 1/12, so they finish in 12 days.

Question 10

P and Q can complete a work in 16 days and 24 days, respectively. They begin the work together, but Q leaves after 6 days. How many more days will P take to finish the remaining work?

Accepted Answer

6 days. P’s rate is 1/16 per day and Q’s rate is 1/24 per day, so together they do 5/48 of the work per day. In 6 days they complete 5/8 of the work, leaving 3/8, which P finishes in 6 days.

Question 11

M and N can complete a certain project together in 36 days. After M works for 20 days, N is left to finish the remaining work by himself in 52 days. How many days would it take N to complete the entire project on his own?

Accepted Answer

72 days. Let M’s and N’s daily work rates be $m$ and $n$. Then $m+n=1/36$. Also, after M works for 20 days, the remaining work is what N completes in 52 days, so $1-20m=52n$. Solving these two equations gives $n=1/72$, so N alone takes 72 days.

Question 12

P, Q, and R can complete a certain work in 24, 36, and 72 days, respectively. How many days will it take for P to finish the work if he receives help from Q and R every fourth day?

Accepted Answer

19 days. P’s 1-day work = $1/24$, Q’s = $1/36$, and R’s = $1/72$. In every 4-day cycle, P works 4 days and gets help from Q and R on the 4th day, so total work per cycle is $3\cdot\frac{1}{24}+\left(\frac{1}{24}+\frac{1}{36}+\frac{1}{72}\right)=\frac{1}{8}+\frac{1}{12}=\frac{5}{24}$. After 4 such cycles, 20 days, the work would exceed 1, so the exact completion occurs on day 19.

Question 13

Pipe A can fill a tank in 18 minutes and Pipe B can fill it in 36 minutes. Both are opened together. After 6 minutes, the rate of Pipe A becomes half and Pipe B’s rate becomes double. How many more minutes are required to fill the tank?

Accepted Answer

6 min. Initially, A fills $1/18$ tank per minute and B fills $1/36$ per minute, so together they fill $1/12$ tank per minute. In 6 minutes they fill $6/12 = 1/2$ tank. After the change, A works at $1/36$ and B at $1/18$, so the combined rate is again $1/12$ tank per minute; thus the remaining half takes 6 more minutes.

Question 14

Tap X and Tap Y can fill a cistern in 12 hours and 15 hours respectively. An outlet pipe Z can empty it in 20 hours. If all three are opened together, how long will it take to fill the empty cistern?

Accepted Answer

10 hours. Tap X fills $\frac{1}{12}$ cistern per hour and Tap Y fills $\frac{1}{15}$ per hour, while Z empties $\frac{1}{20}$ per hour. Net rate = $\frac{1}{12}+\frac{1}{15}-\frac{1}{20}=\frac{1}{10}$ cistern per hour, so the cistern fills in 10 hours.

Question 15

Two pipes A and B can fill a tank in 10 and 15 minutes respectively. After both are opened together for 3 minutes, the rate of pipe A becomes one-third, and pipe B becomes 2.5 times its original rate. In how many more minutes will the tank be full?

Accepted Answer

2 min 30 sec. Initially, A fills $1/10$ tank/min and B fills $1/15$ tank/min, so together they fill $1/6$ tank/min. In 3 minutes, they fill $1/2$ tank. After that, A’s rate becomes $\frac{1}{3}\cdot\frac{1}{10}=\frac{1}{30}$ and B’s rate becomes $2.5\cdot\frac{1}{15}=\frac{1}{6}$, so combined rate is $\frac{1}{5}$ tank/min. Remaining half tank takes $\frac{1/2}{1/5}=2.5$ minutes = 2 min 30 sec.

Question 16

P and Q are hired for a project for ₹1200. P starts the work alone; Q joins when 20% of the work is completed. If Q is 1.5 times as efficient as P, calculate Q's total earnings.

Accepted Answer

₹ 576. Let P's efficiency be 1 unit and Q's efficiency be 1.5 units. P does 20% of the work alone, and the remaining 80% is done together in the ratio 1 : 1.5 = 2 : 3. So Q's share of the total work is $\frac{3}{5}\times 80\% = 48\%$, hence Q earns $48\%$ of ₹1200 = ₹576.

Question 17

A and B together earn ₹1200 for a job. A works the whole time; B joins after 40% of the job is done. B is 1.5 times as efficient as A. Find B's share.

Accepted Answer

₹432. Let A's efficiency be 1 and B's be 1.5. If the total job is 1 unit, A does all of it, while B does only the last 60%, so B's work contribution is $1.5	imes 0.6=0.9$ units and A's is 1 unit. Thus the ratio A:B is $1:0.9=10:9$, so B's share is $1200	imes\frac{9}{19}=₹432$.

Question 18

A boy and a girl are together filling a tank with water. The boy pours 5 liters every 4 minutes, while the girl pours 4 liters every 5 minutes. How much time will it take to fill 82 liters of water in the tank?

Accepted Answer

40 min. The boy's rate is $5/4$ L/min and the girl's rate is $4/5$ L/min. Their combined rate is $5/4+4/5=41/20$ L/min. Time to fill 82 liters is $82\div(41/20)=40$ minutes.

Question 19

If 4 workers take 4 days to build 4 walls, how long will 50 workers take to build 50 walls?

Accepted Answer

4 days. If 4 workers build 4 walls in 4 days, then 1 worker builds 1 wall in 4 days. Therefore, 50 workers will build 50 walls in the same 4 days.

Question 20

P can do a piece of work in 5 days, and Q can do it in 10 days. If they work together for 2 days, how much of the work will be left?

Accepted Answer

40%. P’s one-day work = $1/5$, Q’s one-day work = $1/10$. Together they do $1/5 + 1/10 = 3/10$ of the work per day, so in 2 days they complete $6/10 = 60\%$. Hence, 40% work is left.

Question 21

15 women can do a work in 20 days. 12 men can complete the same work in 10 days. What is the ratio between the efficiency of a man and a woman?

Accepted Answer

5:2. 15 women finish the work in 20 days, so 1 woman's 1-day work is 1/(15×20). Similarly, 12 men finish it in 10 days, so 1 man's 1-day work is 1/(12×10). The ratio of efficiency of a man to a woman is therefore [1/120] : [1/300] = 300:120 = 5:2.

Question 22

X and Y can complete a task in 15 days together. X is 50% more efficient than Y. What percentage of the work is done by X alone?

Accepted Answer

60%. If Y's efficiency is 2 units, then X's efficiency is 3 units because X is 50% more efficient. So together they work in the ratio 3:2, and X's share of the work is 3/(3+2) = 3/5 = 60%.

Question 23

A group of 4 men or 6 women can complete a task in 40 days. Find the time taken by 4 men and 6 women together to complete the task.

Accepted Answer

20 Days. Since 4 men alone finish in 40 days, their rate is $1/40$ task per day. Similarly, 6 women alone also have rate $1/40$ per day, so together their rate is $1/20$ task per day, meaning 20 days.

Question 24

40 men can do a piece of work in 10 days. Find the time required by 25 men to do double the work.

Accepted Answer

32 Days. 40 men working for 10 days complete one job, so total work = 400 man-days. Double the work = 800 man-days. With 25 men, time required = $800/25 = 32$ days.

Question 25

A can do a certain work in the same time in which B and C together can do it. If A and B together can do it in 12 days and C alone can do it in 60 days, then B alone can do it in:

Accepted Answer

30 days. Let the daily work rates of A, B, and C be a, b, and c. Given a = b + c, a + b = 1/12, and c = 1/60. Substituting a = b + c gives 2b + c = 1/12, so 2b + 1/60 = 1/12, which yields b = 1/30.

Question 26

25 workers can do a piece of work in 40 days. Find the percentage of work done by 50 workers in 5 days.

Accepted Answer

25%. Total work = 25 × 40 = 1000 worker-days. Work done by 50 workers in 5 days = 50 × 5 = 250 worker-days. So the fraction completed is 250/1000 = 1/4 = 25%.

Question 27

If 12 men can build a wall in 15 days, in how many days can 18 men complete the same work?

Accepted Answer

10. Total work = 12 × 15 = 180 man-days. If 18 men work on it, days required = 180/18 = 10 days. So the correct answer is 10.

Question 28

If 10 men or 15 women can complete a work in 170 days, how long will 20 men and 20 women take to complete the same work?

Accepted Answer

51 days. If 10 men finish the work in 170 days, then 1 man’s 1-day work is $\frac{1}{10\times170}$. Similarly, 1 woman’s 1-day work is $\frac{1}{15\times170}$. Adding the rates of 20 men and 20 women gives the total daily work, from which the time comes out to 51 days.

Question 29

Two taps can fill a tub in 6 minutes and 4 minutes, respectively. A pipe can empty it in 3 minutes. If all three are kept open simultaneously, when will the tub be full?

Accepted Answer

12 min. The two taps fill at rates of $1/6$ and $1/4$ tub per minute, while the pipe empties at $1/3$ tub per minute. Net rate = $1/6 + 1/4 - 1/3 = 1/12$ tub per minute. So the tub will be full in 12 minutes.

Question 30

Sudarshan can copy 50 pages in 10 hours. Sudarshan and Prakash together can copy 300 pages in 40 hours. In how much time can Prakash copy 25 pages?

Accepted Answer

10 hours. Sudarshan’s rate is 50/10 = 5 pages per hour. Together they copy 300/40 = 7.5 pages per hour, so Prakash’s rate is 2.5 pages per hour. To copy 25 pages, Prakash needs 25/2.5 = 10 hours.

Question 31

The time taken to cover 132 km by car is 1 hour. Find the time taken to cover 88 km by car.

Accepted Answer

40 min. If 132 km takes 1 hour, then speed is 132 km/h. Time for 88 km is $88/132 = 2/3$ hour, which is 40 minutes.

Question 32

A can complete a task in 15 days, and B can complete the same task in 20 days. How long will it take them to complete the task together?

Accepted Answer

8.5 days. A’s rate is $1/15$ work/day and B’s rate is $1/20$ work/day. Together, their rate is $1/15+1/20=7/60$ work/day, so time taken is $60/7\approx 8.57$ days.

Question 33

Suman and Sujata travel the same distance at speeds of 10 km/h and 12 km/h respectively. If Suman takes 36 minutes more than Sujata, the distance traveled by each is:

Accepted Answer

36 km. The difference in times is 36 minutes = 0.6 hour. For the same distance $d$, the time difference is $\frac{d}{10}-\frac{d}{12}$. Solving gives $d\left(\frac{1}{60}\right)=0.6$, so $d=36$ km.

Question 34

A car traveling at a speed of 50 km/h can complete a journey in 8 hours. How long will it take to travel the same distance at 40 km/h?

Accepted Answer

10 h. The distance covered is 50 × 8 = 400 km. At 40 km/h, time taken = 400/40 = 10 hours. So the correct answer is 10 h.

Question 35

The efficiency of A, B and C is in the ratio 2:3:5. A alone can complete the work in 40 days. They all worked together for 5 days and then C left the work. In how many days can A and B together complete the remaining work?

Accepted Answer

6 days. Since A:B:C = 2:3:5 and A alone finishes in 40 days, A's rate is 1/40 work/day, so 2 parts = 1/40 and 1 part = 1/80. Thus B's rate = 3/80 and C's rate = 5/80. Together they work at 2/80 + 3/80 + 5/80 = 10/80 = 1/8 per day, so in 5 days they complete 5/8 of the work; remaining work = 3/8. A and B together work at 1/40 + 3/80 = 1/16 per day, so time needed = (3/8) ÷ (1/16) = 6 days.

Question 36

A, B, and C together can complete a task in 6 days. If A alone takes 12 days and B alone takes 18 days, how long will C alone take?

Accepted Answer

36 days. Their combined rate is $1/6$ work per day. A's rate is $1/12$ and B's rate is $1/18$, so C's rate is $1/6-1/12-1/18=1/36$. Hence C alone takes 36 days.

Question 37

A contractor hires 10 workers who can complete a task in 16 days. After 4 days, he fires 2 workers. How many more days will the remaining workers take to complete the task?

Accepted Answer

15 days. Total work = $10\times16=160$ worker-days. In 4 days, 10 workers do $10\times4=40$ worker-days, leaving $120$ worker-days. After 2 workers are fired, 8 workers remain, so time needed = $120/8=15$ days.

Question 38

Lalit can finish a work in 15 days. Laxman can finish the same work in 25 days. They work together for 5 days. If the rest of the work is finished by Lalit and Deven in 4 days, then in how many days can Deven alone finish the work?

Accepted Answer

20 days. Lalit’s rate is 1/15 and Laxman’s rate is 1/25, so together they do 8/75 of the work per day. In 5 days they complete 40/75 = 8/15, leaving 7/15. Lalit and Deven finish this in 4 days, so their combined rate is 7/60; subtracting Lalit’s rate 1/15 gives Deven’s rate 1/20, so Deven alone takes 20 days.

Question 39

A can complete a task in 30 days, and B can complete the same task in 40 days. They work together for 10 days, and then C joins them and completes the remaining work in 5 days. How long will C alone take to complete the task?

Accepted Answer

40 days. A’s rate is $1/30$ per day and B’s rate is $1/40$ per day, so together they do $7/120$ per day. In 10 days, they complete $7/12$ of the work, leaving $5/12$. In the next 5 days, A, B, and C together finish $5/12$, so C’s rate is $1/40$ per day, meaning C alone takes 40 days.

Question 40

X can complete a task in 12 days, while Y takes 18 days to finish the same task. If they work together for 3 days, what fraction of the work will still remain?

Accepted Answer

7/12. X’s rate is 1/12 per day and Y’s rate is 1/18 per day, so together they do 5/36 of the work per day. In 3 days, they complete 15/36 = 5/12 of the work, so the remaining work is 1 - 5/12 = 7/12.

Question 41

Three pumps, A, B, and C, can fill a reservoir. A fills it in 5 hours, B in 7 hours, and C in 10 hours. When all three pumps are opened together, they operate for 1.5 hours before pump C is closed. How much additional time will it take to completely fill the reservoir after that?

Accepted Answer

47/48 hours. Together, A, B, and C fill at a rate of 1/5 + 1/7 + 1/10 = 31/70 of the reservoir per hour. In 1.5 hours, they fill 93/140, leaving 47/140. After C is closed, A and B fill at 1/5 + 1/7 = 12/35 per hour, so the remaining time is (47/140) ÷ (12/35) = 47/48 hours.

Question 42

X, Y, and Z can complete a project in 20, 40, and 60 days respectively. X works every day, while Y and Z join X every third day. How long will it take to finish the project?

Accepted Answer

15 5 6 days. X’s 1-day work = 1/20, Y’s = 1/40, Z’s = 1/60. In 3 days, work done = 1/20 + 1/20 + (1/20+1/40+1/60) = 1/10 + 13/120 = 25/120 = 5/24. So 24/5 = 4.8 such cycles are needed, i.e. 14 full days and 4/5 of the next cycle. The total time comes to 15 5/6 days.

Question 43

The ratio of efficiencies of workers A and B is 4:3. If A can finish a task in 18 days, in how many days will B finish the same task alone?

Accepted Answer

24 days. Since efficiency ratio A:B = 4:3, their time ratio is 3:4. If A takes 18 days, then B takes $18 \times \frac{4}{3} = 24$ days.

SSC CGL (Prelims) General: Time and Work questions with solutions

Questions