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