Question : P alone can complete a work in 15 days and Q alone can complete the same work in 12 days. They start the work together but after 3 days P leaves the work. How much time will Q take to finish the remaining work?
Option 1: 7.2 days
Option 2: 7.8 days
Option 3: 8.5 days
Option 4: 6.6 days
Correct Answer: 6.6 days
Solution :
P alone can complete a work in 15 days.
⇒ P's 1 day's work = $\frac{1}{15}$
Q alone can complete the same work in 12 days.
⇒ Q's 1 day's work = $\frac{1}{12}$
So, (P + Q)'s 1 day's work = $\frac{1}{15}+\frac{1}{12}=\frac{3}{20}$
⇒ (P + Q)'s 3 days work = $\frac{3}{20}×3=\frac{9}{20}$
Remaining work $=1-\frac{9}{20}=\frac{11}{20}$
So, Q's will complete the remaining work in $\frac{\frac{11}{20}}{\frac{1}{12}}=\frac{33}{5}=6.6$ days
Hence, the correct answer is 6.6 days.
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