Ram and Shyam together can finish a piece of work in 8 days. Both started the work together. After 3 days, Ram fell ill. Shyam alone finished the remaining work in 15 days. How many days would Ram take to finish the work alone?
A10 days
B12 days
C16 days
D24 days
Answer & Solution
Correct answer: B. 12 days
Together they complete $1/8$ of the work per day, so in 3 days they finish $3/8$. The remaining work is $5/8$, and Shyam alone finishes that in 15 days. Hence Shyam's full-work time is $15\times \frac{8}{5}=24$ days, so his rate is $1/24$. Ram's rate is then $1/8-1/24=1/12$. Therefore Ram alone would take 12 days.
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