Question : 12 men or 20 boys can finish a work in 10 days. What part of the same work will be done by 4 men and 4 boys in 4 days?
Option 1: $\frac{49}{75}$
Option 2: $\frac{16}{75}$
Option 3: $\frac{26}{75}$
Option 4: $\frac{59}{75}$
Correct Answer: $\frac{16}{75}$
Solution :
Given: 12 men or 20 boys can finish a work in 10 days.
Here, 12M = 20B
⇒ M : B = 20 : 12 = 5 : 3
12 men can finish a work in 10 days.
Let the total work = 12 × 5 × 10 = 600 units
Now, the work done by 4 men and 4 boys in 4 days
= [(4 × 5) + (4 × 3)] × 4
= 32 × 4
= 128 units
$\therefore$ The required part of the work = $\frac{128}{600}$ = $\frac{16}{75}$
Hence, the correct answer is $\frac{16}{75}$.
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