CUET UG 2025 — General Test Arithmetic

When people work together, their work speeds add up. If someone finishes work in $n$n days, they do $\frac{1}{n}$n1​ work per day.

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B alone finishes work in 30 days.

B's work per day $= \frac{1}{30}$=301​ of the total work

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A and B together finish work in 12 days.

(A + B)'s work per day $= \frac{1}{12}$=121​ of the total work

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Since A and B's speeds add up:

A's work per day $= \frac{1}{12} - \frac{1}{30}$=121​−301​

Finding common denominator (LCM of 12 and 30 is 60):

$$\frac{1}{12} = \frac{5}{60}$$121​=605​

$$\frac{1}{30} = \frac{2}{60}$$301​=602​

A's work per day $= \frac{5}{60} - \frac{2}{60}$=605​−602​

A's work per day $= \frac{3}{60}$=603​

A's work per day $= \frac{1}{20}$=201​

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If A does $\frac{1}{20}$201​ work per day, then A needs 20 days to complete the whole work.

Therefore, A alone can finish the work in 20 days.