CUET UG 2025 — General Test Arithmetic

A and B together complete the job in 24 days, so their combined rate is $\frac{1}{24}$241​ of the job per day.

A alone completes the job in 32 days, so A's rate is $\frac{1}{32}$321​ of the job per day.

B's rate = (A and B together) - (A alone)

$$B's \ rate = \frac{1}{24} - \frac{1}{32}$$B′s rate=241​−321​

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

$$= \frac{4}{96} - \frac{3}{96}$$=964​−963​

$= \frac{1}{96}$=961​ of job per day

Therefore, B alone takes 96 days to complete the full job.

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Both A and B worked together for 8 days.

$$Work \ done = \frac{1}{24} \times 8$$Work done=241​×8

$$= \frac{8}{24}$$=248​

$$= \frac{1}{3}$$=31​

They completed $\frac{1}{3}$31​ of the job in 8 days.

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

$$= \frac{2}{3}$$=32​

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B works alone on the remaining work. B's rate is $\frac{1}{96}$961​ per day.

$$Time = \frac{2}{3} \div \frac{1}{96}$$Time=32​÷961​

$$= \frac{2}{3} \times 96$$=32​×96

$$= \frac{192}{3}$$=3192​

$= 64$=64 days

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