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Time, work and pipes for IBPS PO

Three workers together, a partner who leaves early, men and hours, wages split by work, and pipes with a leak. Time and work at IBPS PO level, solved with the total-work method, with six worked examples and eight practice questions.

7 Oct 2026 8 min read

In this guide
  1. The total-work (LCM) method
  2. The ideas that cover most questions
  3. Worked examples
  4. Common mistakes
  5. Practice set
  6. What to do next

Time and work questions look varied, but almost all of them reduce to one line: work = rate × time. Once every worker and every pipe has a rate in the same units, the question becomes addition, subtraction and division.

In IBPS PO, the topic turns up as standalone arithmetic in the prelims, as one statement in quantity comparison and data sufficiency, and occasionally inside a caselet in the mains. The numbers are chosen to divide cleanly, so a fast method matters more than heavy calculation.

The total-work (LCM) method

  1. Take the total work as the LCM of the given times.
  2. Divide to get each worker's (or pipe's) work per day (or per hour).
  3. Add rates for people working together. Subtract the rate of anything that undoes work, such as a leak.
  4. Time = total work ÷ combined rate.

Why it works: fractions like 1/12 + 1/18 are correct but slow. Choosing the LCM as the total turns every rate into a whole number, so the arithmetic becomes mental. You can pick any total; the LCM is just the one that avoids fractions.

The ideas that cover most questions

IdeaWhat it meansHow to use it
EfficiencyA is 50% more efficient than BRates A : B = 3 : 2, so times are 2 : 3
PairsA+B, B+C and C+A times are givenAdding the three pair-rates gives 2(A + B + C)
Leaving early or joining lateSomeone works fewer days than the totalWrite each person's days, then work done = rate × own days
Man-daysMore people or hours finish fasterM1 × D1 × H1 ÷ W1 = M2 × D2 × H2 ÷ W2
WagesPayment for a shared jobSplit in the ratio of work done, not days present
Pipes and cisternsInlets fill, outlets or leaks emptyInlets are +, outlets are −; the rest is the same method

Why time is inverse to efficiency: if A does 3 units a day and B does 2, the same job takes A two-thirds of B's time. So an efficiency ratio of 3 : 2 is a time ratio of 2 : 3. Flipping the ratio is the step people forget.

Why man-days work: a job needs a fixed amount of labour. Twelve people for ten days is the same labour as twenty-four people for five days, as long as everyone works at the same rate. Hours per day and the size of the job scale the same way.

Worked examples

Example 1 (pairs): A and B can finish a job in 15 days, B and C in 20 days, and A and C in 12 days. How long will all three take together? How long will A take alone?

  • Total work = LCM of 15, 20, 12 = 60 units.
  • Rates: A+B = 4, B+C = 3, A+C = 5. Sum = 12 = 2(A + B + C), so A + B + C = 6 a day.
  • All three: 60 ÷ 6 = 10 days.
  • A = (A + B + C) − (B + C) = 6 − 3 = 3 a day, so A alone takes 60 ÷ 3 = 20 days.

Example 2 (one leaves early): A and B can do a job in 20 and 30 days. They start together, but A leaves 5 days before the job is finished. How long does the job take?

  • Total 60 units. A does 3 a day and B does 2.
  • Let the job take t days. B works all t days; A works t − 5 days.
  • 3(t − 5) + 2t = 60, so 5t = 75 and t = 15 days.
  • Check: A works 10 days (30 units), B works 15 days (30 units). Total 60.

Example 3 (man-days): 12 people working 8 hours a day finish a job in 10 days. How many days will 16 people working 6 hours a day take to finish a job twice as large?

  • 12 × 10 × 8 ÷ 1 = 16 × D × 6 ÷ 2.
  • 960 = 48D, so D = 20 days.

Example 4 (efficiency): A is 50% more efficient than B. Working together, they finish a job in 12 days. How long would B take alone?

  • Rates A : B = 3 : 2, so together they do 5 units a day.
  • Total work = 5 × 12 = 60 units.
  • B alone: 60 ÷ 2 = 30 days. (A alone would take 20 days.)

Example 5 (pipes with an outlet): Pipes A and B can fill a tank in 20 and 30 minutes. Pipe C can empty it in 15 minutes. All three are opened together, and C is closed after 30 minutes. How much longer does the tank take to fill?

  • Total 60 units. Rates: A +3, B +2, C −4.
  • With all three open, the tank gains 3 + 2 − 4 = 1 unit a minute. In 30 minutes it holds 30 units.
  • Remaining 30 units at 3 + 2 = 5 a minute: 6 more minutes.

Example 6 (wages with a helper): A and B can do a job in 10 and 15 days. With C's help, the three finish it in 5 days. The payment for the job is ₹6,000. What is C's share?

  • Total 30 units. A does 3 a day and B does 2. Together, all three do 30 ÷ 5 = 6 a day, so C does 1.
  • In 5 days: A does 15 units, B 10 and C 5.
  • C's share = 5/30 × 6,000 = ₹1,000.

Common mistakes

  • Adding times instead of rates. Always convert to work per day first.
  • Reading efficiency the wrong way. "50% more efficient" means a rate ratio of 3 : 2, and so a time ratio of 2 : 3.
  • Giving the leaver full credit. In Example 2, A works t − 5 days, not t.
  • Splitting wages by days present. Wages follow work done. A faster worker earns more for the same days.
  • Forgetting the minus sign for an outlet or a leak.
  • Using the wrong units. If one pipe is in hours and another in minutes, convert before you take the LCM.
  • Losing count on alternate days. Treat each two-day block as one cycle, count full cycles, then finish the remainder with whoever's turn it is (practice question 6).

Practice set

  1. A, B and C can finish a job in 20, 30 and 60 days. How long will they take together?
  2. A and B take 12 days, B and C take 15 days, and A and C take 20 days. How long will all three take together?
  3. A is twice as efficient as B. Together they finish a job in 14 days. How long would A take alone?
  4. Pipes A and B fill a tank in 12 and 15 hours, and pipe C empties it in 20 hours. How long will the tank take to fill with all three open?
  5. A and B are paid ₹4,500 for a job they do together. A alone would take 12 days and B 18 days. How much does B get?
  6. A and B can do a job in 12 and 18 days. They work on alternate days, starting with A. In how many days is the job finished?
  7. 15 people can finish a job in 16 days. How many people are needed to finish it in 12 days?
  8. A can do a job in 24 days. A works for 6 days, and then B finishes the rest in 12 days. How long would B take to do the whole job alone?

Answers:

  1. 10 days. Total 60: rates 3 + 2 + 1 = 6 a day.
  2. 10 days. Total 60: pair-rates 5 + 4 + 3 = 12 = 2(A + B + C), so 6 a day.
  3. 21 days. Rates 2 : 1, so total = 3 × 14 = 42; A alone takes 42 ÷ 2.
  4. 10 hours. Total 60: 5 + 4 − 3 = 6 an hour.
  5. ₹1,800. Rates 3 : 2 (total 36: A 3, B 2), so B gets 2/5 of ₹4,500.
  6. 14⅓ days. Total 36: A does 3, B does 2, so each two-day cycle does 5. Seven cycles (14 days) do 35. On day 15, A needs 1 more unit at 3 a day, which is ⅓ of a day.
  7. 20 people. 15 × 16 = 240 man-days; 240 ÷ 12 = 20.
  8. 16 days. A does 6/24 = ¼ of the job. B does the remaining ¾ in 12 days, so the whole job takes B 12 ÷ ¾ = 16 days.

What to do next

  • Solve ten time and work questions a day for five days, always starting with "total = LCM".
  • Redo Examples 2 and 5 without looking. Those two patterns (leaving early, closing a pipe) cause the most slips.
  • Move on to speed, distance and time, which uses the same rate × time idea, and revise ratio and partnership for the wage-sharing logic.

A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Institute of Banking Personnel Selection website .

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