CUET UG 2025 — General Test Arithmetic

P and Q together complete the job in 24 days.

P alone completes the job in 32 days.

P's work rate $= \dfrac{1}{32}$=321​ of the job per day

P and Q together work rate $= \dfrac{1}{24}$=241​ of the job per day

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Q's work rate $= \dfrac{1}{24} - \dfrac{1}{32}$=241​−321​

Finding the common denominator (LCM of 24 and 32 is 96):

$$\dfrac{1}{24} = \dfrac{4}{96}$$241​=964​

$$\dfrac{1}{32} = \dfrac{3}{96}$$321​=963​

Q's work rate $= \dfrac{4}{96} - \dfrac{3}{96}$=964​−963​

Q's work rate $= \dfrac{1}{96}$=961​ of the job per day

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They worked together for 8 days.

Work completed $= 8 \times \dfrac{1}{24}$=8×241​

Work completed $= \dfrac{8}{24}$=248​

Work completed $= \dfrac{1}{3}$=31​ of the job

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Remaining work $= 1 - \dfrac{1}{3}$=1−31​

Remaining work $= \dfrac{2}{3}$=32​ of the job

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Days for Q to complete remaining work $= \dfrac{2}{3} \div \dfrac{1}{96}$=32​÷961​

Days $= \dfrac{2}{3} \times 96$=32​×96

Days $= \dfrac{192}{3}$=3192​

Days $= 64$=64

Therefore, Q will take 64 days to complete the remaining job.