CUET UG 2025 — General Test Arithmetic

P completed $\frac{2}{5}$52​ of the work in 12 days.

Q completed the remaining part.

Remaining work $= 1 - \frac{2}{5} = \frac{3}{5}$=1−52​=53​

Q completed $\frac{3}{5}$53​ of the work in 18 days.

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P's work rate per day:

$$= \frac{2/5}{12}$$=122/5​

$$= \frac{2}{5} \times \frac{1}{12}$$=52​×121​

$$= \frac{2}{60}$$=602​

$= \frac{1}{30}$=301​ of the work per day

P alone can complete the entire work in 30 days.

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Q's work rate per day:

$$= \frac{3/5}{18}$$=183/5​

$$= \frac{3}{5} \times \frac{1}{18}$$=53​×181​

$$= \frac{3}{90}$$=903​

$= \frac{1}{30}$=301​ of the work per day

Q alone can complete the entire work in 30 days.

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Combined work rate when P and Q work together:

$$= \frac{1}{30} + \frac{1}{30}$$=301​+301​

$$= \frac{2}{30}$$=302​

$= \frac{1}{15}$=151​ of the work per day

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Days needed to complete the work together:

$$= \frac{1}{\frac{1}{15}}$$=151​1​

$$= 1 \times 15$$=1×15

$= 15$=15 days

Therefore, P and Q working together can complete the work in 15 days.