Question : Working 5 hours a day, A can complete a task in 8 days, and working 6 hours a day, B can finish the same task in 10 days. Working 8 hours daily, they can jointly complete the task in _____.
Option 1: 5 days
Option 2: 3 days
Option 3: 4.5 days
Option 4: 6 days
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Correct Answer: 3 days
Solution :
If a person works in $n$ days working $y$ hours a day, then
One hour's work of that person is $\frac{1}{ny}$ part of the total work.
One hour's work of A $= \frac{1}{(8 × 5)}= \frac{1}{40}$
One hour's work of B $= \frac{1}{(10\times 6)} = \frac{1}{60}$
One hour's work of both A and B = one day's work of A + one day's work of B
= $\frac{1}{40} +\frac{1}{60}$
= $\frac{3+2}{120}$
= $\frac{5}{120}=\frac{1}{24}$
Then the whole work will be done by A and B together in 24 hours.
Working 8 hours a day both A and B can complete the work in = $\frac{24}{8}$ = 3 days
Hence, the correct answer is 3 days.
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