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

Answer 2

Hello Dear.

Let the time taken by the x women and the (x + 10) men be 6a and 5a respectively.

In First Case,
 Work done by the x women in 6a Days = x × 6a
 = 6ax

Work Done by the (x + 10) women in 5a days = (x + 10) × 5a
= 5ax + 50a

∵ Work Done by the Men = Work Done by the Women.
∴ 6ax = 5ax + 50a
⇒ ax = 50a
⇒ x = 50

∴ Number of Women = x = 50
Number of Men = x + 10 = 60

In Second Case,
Number of Women = 1.5x.
= 1.5 × 50.
= 75 Women.

Number of Days taken by the 1.5 x (or 75 women) to Finish the Work = 20 days.

Number of Men = x - 15
= 50 - 15
= 35

Now,
∵ M₁  × D₁ = M₂ ×  D₂

Where, M₁ = Number of Women
D₁ = Number of Days taken by the Women.
M₂ = Number of Men.
D₂ = Number of Days taken by the Men.

∴ 75 × 20 = 35 × D₂
⇒ D₂ = 1500/35
⇒ D₂ = 300/7 Days.
⇒ D₂ = $42 \frac{6}{7}$


∴ Number of Days Required by the (x - 15) men (or 35 men) to complete the Work is 300/7 or  $42 \frac{6}{7}$ Days.


Hope it helps.