Question

9 men or 14 women can construct a wall in 23 days . How long will it take for 6 men and 6 women to do the same work?

Answer 1

9 men or 14 women can construct a wall in 23 days
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So 9 men can do it in 23 days.

1 man can do it in = 23×9 = 207 days.

in 1 day, 1 man can do = 1/207 of the work
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So 14 women can do it in 23 days.

1 woman can do it in = 23×14 = 322 days.

in 1 day, 1 woman can do = 1/322 of the work

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in 1 day, 6 men can do = 6 × 1/207 = 6/207 of the work

in 1 day, 6 women can do = 6 × 1/322 = 6/322 of the work

in 1 day, 6 men and 6 women together can do =
$\frac{6}{207} + \frac{6}{322} \\ \\ = \frac{6 \times 14 + 6 \times 9}{2898} \\ \\ = \frac{84 + 54}{2898} \\ \\ = \frac{138}{2898} \\ \\ = \frac{1}{21}$

Thus, 6 men and 6 women can do 1/21 of the work in 1 day.

to complete it, number of days required = 1 ÷ 1/21 = 1 × 21 = 21 days

Thus, for the same work, it will take 21 days for 6 men and 6 women to finish it.

Answer 2

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9 men or 14 women can construct a wall in 23 days

-----------------

So 9 men can do it in 23 days.

1 man can do it in = 23×9 = 207 days.

in 1 day, 1 man can do = 1/207 of the work

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So 14 women can do it in 23 days.

1 woman can do it in = 23×14 = 322 days.

in 1 day, 1 woman can do = 1/322 of the work

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in 1 day, 6 men can do = 6 × 1/207 = 6/207 of the work

in 1 day, 6 women can do = 6 × 1/322 = 6/322 of the work

in 1 day, 6 men and 6 women together can do =

$\frac{6}{207} + \frac{6}{322} \\ \\ = \frac{6 \times 14 + 6 \times 9}{2898} \\ \\ = \frac{84 + 54}{2898} \\ \\ = \frac{138}{2898} \\ \\ = \frac{1}{21}$

Thus, 6 men and 6 women can do 1/21 of the work in 1 day.

to complete it, number of days required = 1 ÷ 1/21 = 1 × 21 = 21 days

Thus, for the same work, it will take 21 days for 6 men and 6 women to finish it.