A and B together can do a job in 2 days; B and C can do it in 4 days, and A…

2023

A and B together can do a job in 2 days; B and C can do it in 4 days, and A and C in 2(2/5) days. The number of days required for A to do the job alone is:

  1. A.

    1

  2. B.

    3

  3. C.

    6

  4. D.

    12

Attempted by 21 students.

Show answer & explanation

Correct answer: B

Concept: In work-rate problems, each person's contribution is expressed as the fraction of the job completed in one day. When three overlapping pair-rates are given (A+B, B+C, A+C), adding all three counts every individual's rate exactly twice, so their sum equals 2×(A+B+C). Halving that total gives the combined one-day rate of all three, and subtracting any one given pair's rate isolates the third person's own rate — whose reciprocal is the number of days that person needs alone.

Application:

  1. Let A, B, C denote the fraction of the job each does in one day. Given: A + B = 1/2, B + C = 1/4, and A + C = 5/12.

  2. Add all three equations: 2(A + B + C) = 1/2 + 1/4 + 5/12 = 6/12 + 3/12 + 5/12 = 14/12 = 7/6, so A + B + C = 7/12.

  3. Subtract the B + C equation from this total: A = 7/12 − 1/4 = 7/12 − 3/12 = 4/12 = 1/3.

  4. A's one-day rate of 1/3 means A alone completes the job in 3 days.

Cross-check: B = 1/2 − 1/3 = 1/6 and C = 1/4 − 1/6 = 1/12. Checking A + C = 1/3 + 1/12 = 4/12 + 1/12 = 5/12, which matches the given data, confirming the result.

Explore the full course: Cognizant Preparation