CUET UG 2025 — General Test Arithmetic

When solving work problems, work rate represents how much work someone completes in 1 day. If someone finishes work in 10 days, their work rate is $\frac{1}{10}$101​ per day.

Work rate $= \frac{1}{\text{Time taken to complete whole work}}$=Time taken to complete whole work1​

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Let $b$b = B's work rate (portion of work B does in 1 day)

Let $a$a = A's work rate (portion of work A does in 1 day)

Let $c$c = C's work rate (portion of work C does in 1 day)

Given that A, B, and C together finish the work in 40 days, their combined work rate is $\frac{1}{40}$401​ of the work per day.

$$a + b + c = \frac{1}{40}$$a+b+c=401​

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Given that A and C together can do twice as much work as B alone:

$$a + c = 2b$$a+c=2b

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Substituting $a + c = 2b$a+c=2b into the first equation:

$$2b + b = \frac{1}{40}$$2b+b=401​

$$3b = \frac{1}{40}$$3b=401​

$$b = \frac{1}{120}$$b=1201​

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If B's work rate is $\frac{1}{120}$1201​ per day, then B completes the whole work in 120 days.

Therefore, the answer is 120 days.