Question

- 4 men and 6 women working together can complete the work within 10 days. 3 men and 7 women working together will complete the same work within 8 days. in how many days 10 women will complete this work?

Answer 1

The answer of the question above is....... 2 days

Answer 2

Answer:

10 women need 5 days to complete work.

Step-by-step explanation:

Given : 4 men and 6 women working together can complete the work within 10 days. 3 men and 7 women working together will complete the same work within 8 days.

To find : In how many days 10 women will complete this work?

Solution :

Let men denote by m and women denote by w,

4 men and 6 women working together can complete the work within 10 days.

i.e. In 1 day, they work $4m+6w=\frac{1}{10}$ ......(1)

3 men and 7 women working together will complete the same work within 8 days.

i.e. In 1 day, they work $3m+7w=\frac{1}{8}$ .....(2)

Multiply (1) by 3 and (2) by 4,

$12m+18w=\frac{3}{10}$

$12m+28w=\frac{4}{8}$

Subtract them,

$-10w=\frac{24-40}{80}$

$-10w=-\frac{16}{80}$

$10w=\frac{1}{5}$

Therefore, 10 women need 5 days to complete work.