Question

Four men can do a piece of work in 6 days, while 3 women can complete the same work in 16 days. In how many days 1 man and 2 women working together can complete the work?

Answer 1

Given :  Four men can do a piece of work in 6 days, while 3 women can complete the same work in 16 days

To Find : In how many days 1 man and 2 women working together can complete the work

Solution:

4 men can do a piece of work in 6 days

=> Total work = 4 * 6 = 24 Man days

3 women can complete the same work in 16 days.

=>  Total work = 3 * 16 = 48 Woman days

24 Man days =  48 Woman days

=> 1 Man day  = 2 Woman days

1 man and 2 women working together  1 day work  = 1 Man + 2 Woman day

= 1 Man + 1Man

= 2 Man days

Total work =   24 Man days

=> Number of days = 24/2  = 12

1 man and 2 women working together can complete the work  in 12 days

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Answer 2

Given:

Four men can do a piece of work in 6 days, while 3 women can complete the same work in 16 days

To find:

In how many days 1 man and 2 women working together can complete the work?

Solution:

Let's assume,

"M" → represents the no. of man

"W" → represents the no. of woman

We have a formula as follows:

$\boxed{\bold{M_1 \times D_1 = M_2 \times D_2 }}$

Since the we are given that work done by 4 men and 3 women are same, so by using the above formula, we get

$4M \times 6 = 3W\times 16$

$\implies M = \frac{3W \times 16}{4\times 6}$

$\implies M = 2W$ ...... (i)

From (i), we get

1M + 2W = 1 (2W) + 2W = 2W + 2W = 4W

Now, using the above formula again we will find the no. of days 4W will take to complete the work if 3W takes 16 days to complete it.

∴ $3W \times 16 = 4W \times D_2$

$\implies D_2 = \frac{3W \times 16}{4W}$

$\implies D_2 = \frac{3 \times 16}{4}$

$\implies D_2 = 3 \times 4$

$\implies \bold{D_2 = 12}$

Thus, 1 man and 2 women working together can complete the work in → 12 days.

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