Question : Suresh alone can do work in 10 days working 1 hour a day. Balu alone can do the same work in 2 days working 5 hours a day. How many hours do they need to work together in a day to complete the same work in 10 days?
Option 1: 1.5 hours
Option 2: 0.5 hours
Option 3: 1 hour
Option 4: 2 hours
Correct Answer: 0.5 hours
Solution :
Total time taken by Suresh to do the work = 10 × 1 = 10 hours
⇒ Part of the work done by Suresh in an hour = $\frac{1}{10}$
Total time taken by Balu to do the work = 5 × 2 = 10 hours
⇒ Part of the work done by Balu in an hour = $\frac{1}{10}$
So, part of the work done by Suresh and Balu together in a day = $\frac{1}{10}$ + $\frac{1}{10}$ = $\frac{1+1}{10}$ = $\frac{1}{5}$
$\therefore$ Total time Suresh and Balu took to do the work = $\frac{1}{\frac{1}{5}}=5$ hours = 0.5 hours per day for 10 days
Hence, the correct answer is 0.5 hours.
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