Question

Five Men can paint a building in 20 days, 8 Women can paint the same building in 25 days and 10 Boys can paint it in 30 days. If a team has 2 Men, 6 Women and 5 Boys, how long will it take to paint the building?

• A.
  12 days
• B.
  13 days
• C.
  14 days
• D.
  15 days

Answer 1

The correct option is D

15 days
5 men in 20 days = 100 men days
8 women in 25 days = 200 woman days
10 boys in 30 days = 300 boy days

$\therefore$ It means 100MD = 200WD = 300BD

or 1 men day = 3 boy days;
1 woman day = 1.5 boy days

So, 2 men, 6 women and 5 boys
= 2 x 3 + 6 x 1.5 + 5 = 20 boys

So, 20 boys deployed to complete the task which will get completed in 300/20 = 15 days

Alternate Solution:

$[2\times \frac{1}{100}+6\times \frac{1}{200}+5\times \frac{1}{300}]x=1$

$\therefore x=15$