A can do a piece of work in 4 hours. B and C together can do the same work in 3 hours. A and C together can do the same work in 2 hours. How long will B alone take to do the work?

Question

Question

This question was previously asked in

CSIR CERI JSA Official Paper-I (Held On: 2022)

Answer 1

Given:

Time taken by A to complete the work = 4 hours.

Time taken by B and C together to complete the work = 3 hours.

Time taken by A and C together to complete the work = 2 hours.

Calculation:

Let the total work be the LCM of 4, 3, and 2, which is 12 units.

Efficiency of A = Total work / Time taken by A = 12 / 4 = 3 units/hour.

Efficiency of (B + C) = Total work / Time taken by (B + C) = 12 / 3 = 4 units/hour.

Efficiency of (A + C) = Total work / Time taken by (A + C) = 12 / 2 = 6 units/hour.

We have the following equations:

A = 3 --- (1)

B + C = 4 --- (2)

A + C = 6 --- (3)

From equation (1) and equation (3):

3 + C = 6

C = 3 units/hour.

From equation (2):

B + 3 = 4

B = 1 unit/hour.

Time taken by B alone to do the work = Total work / Efficiency of B

Time taken by B alone = 12 / 1 = 12 hours.

∴ B alone will take 12 hours to do the work.

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