Question : A can do a piece of work in 20 days and B in 30 days. They work together for 7 days and then both leave the job. Then C alone finishes the remaining work in 10 days. In how many days will C finish the full work?
Option 1: 25 days
Option 2: 30 days
Option 3: 24 days
Option 4: 20 days
Correct Answer: 24 days
Solution :
Given: A can do a piece of work in 20 days and B in 30 days. They work together for 7 days and then both leave the job.
The total work of A and B is LCM of (20, 30) = 60 units
So, the efficiency of A $=\frac{60}{20} = 3$
Efficiency of B $=\frac{60}{30} = 2$
Total work done by A and B in 7 days = (3 + 2) × 7 = 5 × 7 = 35 units
The remaining work is 60 – 35 = 25, which is done by C in 10 days.
(Efficiency of C) × 10 = 25
⇒ Efficiency of C = $\frac{5}{2}$
Now, the time taken by C to complete the whole work is $\frac{60}{\frac{5}{2}}$ = 24 days
Hence, the correct answer is 24 days.
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