Raman can do a piece of work in 45 days and Anju can do the same work in 75 days. After working together for 12 days, Anju stops working. How many days will Raman take to complete the remaining work?
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$25.8$
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$26.3$
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$25.5$
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$25.1$
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$None of these$
A
Correct answer
Explanation
Raman's rate = 1/45 work per day. Anju's rate = 1/75 work per day. Combined rate = 1/45 + 1/75 = (5 + 3)/225 = 8/225 per day. In 12 days together, they complete 12 × 8/225 = 96/225 = 32/75 of work. Remaining work = 1 - 32/75 = 43/75. Raman alone does (43/75) × 45 = 43 × 3/5 = 129/5 = 25.8 days. Option A matches.