Question : Working 6 hours a day, Raman can complete a piece of work in 24 days. How many hours a day should he work to finish the work in 18 days?
Option 1: 8 hours
Option 2: 10 hours
Option 3: 12 hours
Option 4: 16 hours
Correct Answer: 8 hours
Solution :
Given:
Working 6 hours a day, Raman can complete a piece of work in 24 days.
We know,
$\frac{M_{1}D_{1}H_{1}}{W_{1}} = \frac{M_{2}D_{2}H_{2}}{W_{2}}$, where $M$ = number of men , $D$ = number of days, $W$ = amount of work done, and $H$ = hours per day.
Here,
$M_{1} = M_{2} = 1$
$W_{1} = W_{2} = W$
$D_{1} = 24$
$D_{2} = 18$
$H_{1} = 6$
Now, applying the values in the above equation:
$1 \times 24 \times 6 = 1 \times 18 \times H_{2}$
⇒ $H_{2} = 8$
Hence, the correct answer is 8 hours.
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