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Time & Work

If 3 men or 4 women or 6 boys can finish a work in 135 days workin 8 hours a day. The number of days taken by 12 men, 8 women or 18 boys working 12 hours a day will be.

Option:
A. 13.5 days.
B. 12 days.
C. 10 days.
D. 8 days.
Answer: C . 10 days.

Justification:

By hypothesis,
3 men = 4 women = 6 boys
1 man = 2 boys, 1 women = $3/2$ boys.
12 men + 8 women + 18 boys
= 12 x 2 boys + 8 x ${3/2}$boys + 18 boys
24 boys + 12 boys + 18 boys = 54 boys.
Now, 6 boys working in 8 hours a day can finish the work in = 135 days.
1 boy working in 1 hour a day can finish the work in = 135 x 6 x 8
54 boys working 12 hours a day can finish the work in = ${135 × 6 × 8}/{54 × 12}$ = 10 days
 

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