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CAT Quant

CAT time and work practice questions

Time and work problems look different on the surface (workers, pipes, machines) but they share one idea: express each worker's output as a rate, add the rates and invert to get time. When the numbers are awkward, work in units such as man days or the LCM of the days given. Pipes and cisterns are the same problem with some pipes working against you.

Key ideas

  • Rate = 1 / time. Rates of workers add up when they work together.
  • Total work = number of workers x days x efficiency. Use man days when workers are identical.
  • Pick the LCM of the given times as the total work to avoid fractions.
  • An emptying pipe or a leak has a negative rate.
  • If A is k times as efficient as B, A takes 1/k of B's time.

Common traps

  • Adding times instead of rates.
  • Forgetting workers who join or leave part way, so the remaining work changes.
  • Mixing up the direction of a pipe that empties the tank.

Practice questions with solutions

Try each question first, then open the solution. Aim for about 90 seconds per question.

  1. A can finish a job in 10 days and B in 15 days. In how many days can they finish it together?

    • A 6 days
    • B 5 days
    • C 8 days
    • D 12.5 days
    Show answer and solution

    Answer: A. 6 days

    Rate = 1/10 + 1/15 = 1/6, so 6 days.

  2. A and B together can do a job in 12 days, and A alone can do it in 20 days. How long will B take alone?

    • A 24 days
    • B 32 days
    • C 36 days
    • D 30 days
    Show answer and solution

    Answer: D. 30 days

    B's rate = 1/12 - 1/20 = 1/30, so B takes 30 days.

  3. 8 men can complete a job in 18 days. After 6 days, 4 more men join. In how many more days is the job finished?

    • A 6 days
    • B 9 days
    • C 8 days
    • D 10 days
    Show answer and solution

    Answer: C. 8 days

    Total = 144 man days. Done in 6 days = 48. Remaining = 96 man days. With 12 men this takes 8 days.

  4. Pipe A fills a tank in 6 hours and pipe B empties it in 12 hours. If both are opened together, how long does it take to fill the empty tank?

    • A 8 hours
    • B 9 hours
    • C 12 hours
    • D 18 hours
    Show answer and solution

    Answer: C. 12 hours

    Net rate = 1/6 - 1/12 = 1/12 per hour, so 12 hours.

  5. A is twice as efficient as B. Together they finish a job in 12 days. How long would A take alone?

    • A 24 days
    • B 18 days
    • C 36 days
    • D 16 days
    Show answer and solution

    Answer: B. 18 days

    Together they have 3 units of efficiency and take 12 days, so total work = 36 units. A has 2 units per day, so A takes 18 days.

  6. A and B can do a job in 12 days, B and C in 15 days, and A and C in 20 days. How long will all three take working together?

    • A 10 days
    • B 9 days
    • C 12 days
    • D 8 days
    Show answer and solution

    Answer: A. 10 days

    Adding the three rates: 2(A + B + C) = 1/12 + 1/15 + 1/20 = 1/5. So A + B + C = 1/10, which is 10 days.

  7. A can do a job in 24 days. He works for 6 days and then B finishes the rest in 12 days. How many days would B take to do the whole job alone?

    Type in the answer (no options).

    Show answer and solution

    Answer: 16

    After 6 days, 3/4 of the job remains. B does 3/4 in 12 days, so the full job takes 16 days.

  8. A tank is filled by a pipe in 8 hours. Because of a leak it takes 24 hours to fill. How many hours would the leak alone take to empty the full tank?

    Type in the answer (no options).

    Show answer and solution

    Answer: 12

    With the leak the net filling rate is 1/24. The pipe alone fills at 1/8, so the leak drains at 1/8 - 1/24 = 1/12 per hour. It empties a full tank in 12 hours.

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