Question

The ratio of time taken to complete a work by x women to x+10 men is 6 :5. If 1.5x women take 20days to finish the work find out the no of days required by x-15 men?

Answer 1

ratio of time taken to complete a work by x women and (x + 10)men is 6:5
Let x women take time = 6y
(x + 10) men take time = 5y
∴ work done by women = work done by men
x × 6y = (x + 10) × 5y
6xy = 5xy + 50y
xy = 50y
x = 50

∵ we know, M₁N₁ = M₂N₂
here, M shows number of workers .
N shows number of days .
Given, M₁ = 1.5x = 15 × 50 = 75
N₁ = 20 days
M₂ = (x - 15) = 50 - 15 = 35
N₂ = ?
∴ 75 × 20 = 35 × N₂
N₂ = 75 × 20/35 = 300/7 days

Hence, number of days required = 300/7 days