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Time and Work questions for IPMAT, with solutions

10 free Time and Work practice questions for IPMAT Indore, Rohtak and JIPMAT, each with the answer and a full worked solution. No sign-in. Try each one first, then open the solution. The lessons for this chapter are in Time and Work on Learn.

1. Question 1Type the answerWritten by IPMATwayPipes and Cisterns

   A $2400$-litre tank has an inlet that adds $20$ litres a minute and an outlet that removes $12$ litres a minute. Both are opened on the empty tank. In how many hours will it be full?

   Show the answer and solution

   Answer: 5

   The inlet adds $20$ litres a minute and the outlet removes $12$. Net gain $=20-12=8$ litres a minute. The $2400$-litre tank fills in $\frac{2400}{8}=300$ minutes. In hours that is $\frac{300}{60}=5$ hours.

2. Question 2Type the answerWritten by IPMATwayWork and Efficiency

   $20$ workers can finish a job in $30$ days. After $12$ days, $5$ workers leave. In how many more days will the remaining workers finish the job?

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   Answer: 24

   The whole job is $20\times30=600$ worker-days. In the first $12$ days, $20$ workers do $240$ worker-days. Work left $=600-240=360$ worker-days. With $20-5=15$ workers it takes $\frac{360}{15}=24$ more days.

3. Question 3Type the answerWritten by IPMATwayPipes and Cisterns

   Pipes A and B can fill a tank in $20$ minutes and $30$ minutes respectively, and pipe C can empty the full tank in $15$ minutes. If all three are opened on the empty tank, in how many minutes will it be full?

   Show the answer and solution

   Answer: 60

   Take the tank as $60$ units (LCM of $20$, $30$, $15$). A adds $\frac{60}{20}=3$ units a minute, B adds $\frac{60}{30}=2$, and C removes $\frac{60}{15}=4$. Net gain $=3+2-4=1$ unit a minute. The empty tank fills in $\frac{60}{1}=60$ minutes.

4. Question 4Type the answerWritten by IPMATwayPipes and Cisterns

   A leak can empty a full tank in $8$ hours. An inlet pipe fills water at $6$ litres per minute. When the tank is full, the inlet is opened while the leak continues, and the tank now empties in $12$ hours. What is the capacity of the tank, in litres?

   Show the answer and solution

   Answer: 8640

   Let the capacity be $C$ litres. The leak empties $\frac C8$ litres an hour. The inlet adds $6\times60=360$ litres an hour. The net loss is $\frac C{12}$ an hour. So $\frac C8-360=\frac C{12}$, giving $C\left(\frac18-\frac1{12}\right)=\frac C{24}=360$. Hence $C=8640$ litres.

5. Question 5Type the answerWritten by IPMATwayWork and Efficiency

   A can finish a job in $24$ days. A works alone for $6$ days; then B joins and together they finish the remaining work in $9$ days. In how many days can B alone finish the whole job?

   Show the answer and solution

   Answer: 24

   After 6 days A has done $\frac14$. The remaining $\frac34$ takes 9 days together, so the joint rate is $\frac{1}{12}$ per day. Subtract A's $\frac1{24}$: B does $\frac1{24}$ per day, i.e. 24 days alone.

6. Question 6Multiple choiceWritten by IPMATwayWork and Efficiency

   $6$ men and $8$ boys can do a job in $10$ days, while $26$ men and $48$ boys can do it in $2$ days. In how many days will $10$ men and $20$ boys do it?

   1. A.$4\frac{2}{3}$ days
   2. B.$10$ days
   3. C.$4\frac{2}{5}$ days
   4. D.$5$ days
   Show the answer and solution

   Answer: D. $5$ days

   Equate the work: $60m+80b=52m+96b$, so $8m=16b$, a man does the work of 2 boys. The first team is 20 boys' worth and takes 10 days: 200 boy-days. The new team is $10\times2+20=40$ boys' worth: $5$ days.

7. Question 7Type the answerWritten by IPMATwayWork and Efficiency

   A garrison of $1200$ soldiers has food for $28$ days. After $4$ days a reinforcement arrives, and the remaining food now lasts only $16$ more days. How many soldiers are in the reinforcement?

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   Answer: 600

   After 4 days the food left would feed 1200 soldiers for 24 days, i.e. $28800$ soldier-days. Lasting 16 days, it feeds 1800 soldiers, so $600$ arrived.

8. Question 8Multiple choiceWritten by IPMATwayPipes and Cisterns

   Pipes A and B can fill an empty tank in $6$ hours and $8$ hours respectively; pipe C can empty a full tank in $12$ hours. A and B are opened together, and C is also opened after the first hour. How long after A and B were opened is the tank full?

   1. A.$3\frac37$ hours
   2. B.$4\frac45$ hours
   3. C.$4\frac25$ hours
   4. D.$3\frac25$ hours
   Show the answer and solution

   Answer: C. $4\frac25$ hours

   Per hour A fills $\frac16$, B fills $\frac18$ and C empties $\frac1{12}$ of the tank. With A and B alone the rate is $\frac16+\frac18=\frac7{24}$; with C also open it is $\frac7{24}-\frac2{24}=\frac5{24}$. In the first hour $\frac7{24}$ of the tank is filled, leaving $\frac{17}{24}$. At $\frac5{24}$ per hour this takes $\frac{17}5=3.4$ h. Total time $=1+3.4=4.4=4\frac25$ hours. Ignoring C gives $3\frac37$, opening C at the start gives $4\frac45$, and forgetting the first hour gives $3\frac25$.

9. Question 9Multiple choiceWritten by IPMATwayWages and Work Share

   A and B can finish a job in $12$ and $15$ days respectively. They start together; after $4$ days C joins them, and the three finish the job in $2$ more days. The total payment of ₹$6000$ is shared in proportion to the work done. What is C's share?

   1. A.₹$600$
   2. B.₹$1500$
   3. C.₹$2400$
   4. D.₹$1800$
   Show the answer and solution

   Answer: A. ₹$600$

   Let the job be $60$ units (LCM of $12$ and $15$). A does $5$ units a day and B $4$ units a day. A and B work all $6$ days: $6 \times 9 = 54$ units. The job is $60$ units, so C did $60 - 54 = 6$ units in his $2$ days (rate $3$ units a day, i.e. alone he would take $20$ days). Payment by work: A $30$ units, B $24$ units, C $6$ units out of $60$. C's share $= \frac{6}{60} \times 6000 =$ ₹$600$ (A gets ₹$3000$, B ₹$2400$).

10. Question 10Multiple choiceWritten by IPMATwayWages and Work Share

    $3$ men and $4$ women together earn ₹$3450$ in $5$ days. $5$ men and $2$ women together earn ₹$3480$ in $4$ days. How much will $2$ men and $3$ women earn together in $6$ days?

    1. A.₹$3420$
    2. B.₹$2880$
    3. C.₹$2400$
    4. D.₹$1920$
    Show the answer and solution

    Answer: B. ₹$2880$

    Let a man earn ₹$m$ and a woman ₹$w$ per day. First group per day: $3450 / 5 = 690$, so $3m + 4w = 690$. Second group per day: $3480 / 4 = 870$, so $5m + 2w = 870$. Double the second: $10m + 4w = 1740$; subtract the first: $7m = 1050$, so $m = 150$ and $w = (690 - 450)/4 = 60$. $2$ men and $3$ women earn $2 \times 150 + 3 \times 60 = 480$ a day, so in $6$ days ₹$2880$. Forgetting to divide by the number of days first gives wrong equations.