Question

A work gets completed in 10 days if either 5 men and 4 women work on it or 7 men and 3 women work on it. how long will 10 men take to complete the work?a work gets completed in 10 days if either 5 men and 4 women work on it or 7 men and 3 women work on it. how long will 10 men take to complete the work?a work gets completed in 10 days if either 5 men and 4 women work on it or 7 men and 3 women work on it. how long will 10 men take to complete the work?

Answer 1

13 days will taken to complete the work by 10 men

Answer 2

Answer: 13 days

Step-by-step explanation:

Strength = $\frac{Work}{Time}$ (Similar to Speed equation)

Work to be done = y

Strength of 1 man = x

Strength of 1 woman = a (soon to be expressed in terms of x)

5x + 4a = 7x + 3a (Both terms are strength)

On subtracting LHS from RHS,

2x - a = 0

2x = a

Strength of 1 woman = 2x

Strength of 1 man = x

NOTE: Contrary to many sums, in this sum a woman's strength is more than a man's.

5x + 8x = 7x + 6x

13x = 13x

Hence proven a woman's strength is twice that of a man's.

Strength =$\frac{Work}{Time}$

13x = Strength

y = Work

10 = Time

13x = $\frac{y}{10}$

Question: 10x = $\frac{y}{?}$

13x = $\frac{y}{10}$

10x = $\frac{y}{?}$

13x($\frac{10}{13}$) = $\frac{y}{10}$($\frac{10}{13}$)

10x =  $\frac{y}{10}$($\frac{10}{13}$)

10x = $\frac{y}{13}$

Therefore, it will take 10 men 13 days to complete the work.