Question

8. 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?

Answer 1

Answer:

5:6

Step-by-step explanation:

let work done by man in 1 day= m

work done by boy in 1 day= b

So,

5m + 12b = 1/4

and,

7m + 6b = 1/5 → 14m + 12b = 2/5 ((multiply whole eq. by 2))

Subtract the two eq.

14m + 12b = 2/5

-5m - 12b = -1/4

⇒9m = 2/5 - 1/4 = (8-5) / 20 = 3 / 20

m = (3/20) (1/9) = 1 / (20×3) = 1/60

⇒ 12b = 1/4 - ( 5 × 1/60 ) = 1/4 - 1/12 = (3-1) / 12 = 2/12 = 1/6

⇒ b = 1/6 × 1/12 = 1/72

∴ 1 boy will do the work in 72 days and 1 man will do the work in 60 days

⇒ Ratio between efficiencies of man : boy = 60 : 72 = 5 : 6