If 8 men or 12 women can do a piece of work in 25 days, in how many days can the same work be done by 6 men and 11 women?
If 8 men or 12 women can do a piece of work in 25 days, in how many days can the same work be done by 6 men and 11 women?
1). 15 days
2). 12 days
3). 18 days
4). 22 days
1 answers
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.