Question

8 men or 12 women can do a job in 25 days in what time can 6women and11 women do it​

Answer 1

Answer:

Given:

If 8 men or 12 women can do a piece of work in 25 days.

Formula used:

M1 × D 1 × T1 × W2 = M2 × D 2 × T2 × W1

Calculation:

According to the question

8 men take 25 days ⇒ 1 man will take 8 × 25 = 200 days.

12 women take 25 days ⇒ 1 woman will take 12 × 25 = 300 days.

∴ 1 man’s one day’s work = (1/200)

⇒ 6 men’s one day’s work = (6/200)

Similarly,

1 woman’s one day’s work = (1/300)

⇒ 11 women’s one day’s work = (11/300)

Now,

11 women’s and 6 men’s one day’s work = (11/300) + (6/200)

= 1/15

∴ They will take 15 days to complete the work.

Alternate Method

We know that,

If M1 persons can do W1 work in D1 days working T1 hours per day and M2 persons can do W2 work in D2 days working T2 hours per day, then the relationship between them is:

M1 × D 1 × T1 × W2 = M2 × D 2 × T2 × W1

Given that, 8 men or 12 women can do a piece of work in 25 days,

⇒ (8m × 25) = (12w × 25)

⇒ m = (3/2) w

Now, let the required work will be done in ‘x’ days by 6 men and 11 women.

⇒ (8m × 25) = (6m + 11w) × x

Eliminating one variable by putting the value of ‘m’ from our result,

⇒ {8 × (3/2) w × 25} = {6 × (3/2) w + 11w} × x

⇒ 12w × 25 = 20w × x

⇒ x = 15 days

Hence, the required time to finish the work is 15 days.