Question

12 men take 18 days to complete a job whereas 12 women in 18 days can complete 3/4 of the sam job. How many days will 10 men and 8 women together take to complete the same job?

Answer 1

Please see the attachment

Answer 2

10 men and 8 women together take to complete the same job in $13\frac{1}{2}\ days$

Solution:

In 18 days, 12 men can do 1 complete work

And in 18 days, 12 women can do 3/4th of the work

Since time and the number of persons is the same is both cases,

$\text{1 women\s daily\ work } = \frac{3}{4}th \text{ of 1 man's daily work }$

Therefore,

$\text{8 women\ daily\ work } = \frac{3}{4} \times 8 = 6\ men\ daily\ work$

How many days will 10 men and 8 women together take to complete the same job?

10 men + 8 women = 10 men + 6 men = 16 men

12 men can do the work in 18 days

Thus, 16 men can do the work in:

$18 \times \frac{12}{16} = \frac{27}{2} = 13\frac{1}{2}$

Thus, 10 men and 8 women together take to complete the same job in $13\frac{1}{2}\ days$

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