2 men and 3 women can together complete a piece of work in 4 days and 3 men and 2 women together can complete work in 3 days. In how many days 10 women will complete this work?a)9 daysb)6 daysc)7 daysd)12 dayse)10 daysCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

2m + 3w = 4, 3m + 2w = 3
So 4(2m + 3w) = 3(3m + 2w)
8m + 12w = 9m + 6w
6w = 1m
Given 2m + 3w = 4, so 2*(6w) + 3w = 4, so 15 women in 4 days, so 10 women in (15*4)/10 = 6 days

Answer

2m + 3w = 4, 3m + 2w = 3
So 4(2m + 3w) = 3(3m + 2w)
8m + 12w = 9m + 6w
6w = 1m
Given 2m + 3w = 4, so 2*(6w) + 3w = 4, so 15 women in 4 days, so 10 women in (15*4)/10 = 6 days

Answer

Given:
- 2 men + 3 women complete work in 4 days
- 3 men + 2 women complete work in 3 days

To find:
- time taken by 10 women to complete the same work

Assumption:
Let's assume that 1 man's work in 1 day = m and 1 woman's work in 1 day = w

Solution:
From the given information, we can form the following equations:
- 2m + 3w = 1/4 ---(1)
- 3m + 2w = 1/3 ---(2)

We need to find out how much work 10 women can do in 1 day. Let's assume it to be x.

So, 10w = x ---(3)

Now, we can use equations (1) and (2) to find out the value of m and w.

Solving equations (1) and (2), we get:
m = 1/20 and w = 1/30

Substituting the values of m and w in equation (3), we get:
10w = x
10 * (1/30) = x
x = 1/3

Therefore, 10 women can complete 1/3rd of the work in 1 day.

To complete the entire work, they will take:
= 1 / (1/3 * 10)
= 3 days

Hence, the correct answer is option (B) 6 days.

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