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

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SSC GD Constable Memory Based Test (9 Feb 2023 Shift 1)

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Answer 1

Given:

A can do a work = 4 hours.

B and C can do a work = 3 hours.

A and C can do a work = 2 hours.

Concept used:

If a person can complete a work in x hours, part of work done by that person in one hour = \(\dfrac{1}{x}\)

Calculations:

A's one hour work = \(\dfrac{1}{4}\)

(B and C)'s one hour work = \(\dfrac{1}{3}\)

(A and C)'s one hour work = \(\dfrac{1}{2}\)

According to problem,

Part of work done by C, \(\dfrac{1}{C}\) = \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\)

= \(\dfrac{2-1}{4}\)

= \(\dfrac{1}{4}\)

So, C can complete the work in 4 hours.

Now, again, \(\dfrac{1}{B}\) = \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\)

= \(\dfrac{4-3}{12}\)

= \(\dfrac{1}{12}\)

So, B can complete the work in 12 hours.

The answer is 12 hours.

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