Question : 22 boys, working together, can complete a work in 10 days, whereas 25 boys and 12 girls take 8 days to complete the same work. In how many days can only 6 girls, working together, complete the same work?
Option 1: 170
Option 2: 177
Option 3: 175
Option 4: 176
Correct Answer: 176
Solution :
Number of days taken by 22 boys to complete a work = 10 days
Number of days taken by 25 boys and 12 girls to complete the same work = 8 days
Let the efficiency of a boy = B
The efficiency of a girl = G
Total work = 22 × 10 × B = (25 × B + 12 × G) × 8
⇒ 20 × B = 96 × G
⇒ $\frac{\text{B}}{\text{G}} = \frac{24}{5}$
Let B = 24k and G = 5k
So total work = 22 × 10 × 24k
The efficiency of a girl = 5k
So, the required days = $\frac{22 × 10 × 24\text{k}}{5\text{k} × 6}$ = 22 × 8 = 176 days
Hence, the correct answer is 176 days.
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