Sixteen men and twelve women can complete a work in 8 days, if 20 men

1.	Sixteen men and twelve women can complete a work in 8 days, if 20 men can complete the same work in 16 days, in how many days 16 women can complete the same piece of work ?1). 122). 83). 104). 15
Answer» Solution Let work done by 1 man be $X$ and 1 woman be $y$ Now, 16 men and 12 women complete work in 8 days. => $16X + 12y = \FRAC{1}{8}$ ---------Eqn(i) Also, $20x = \frac{1}{16}$ => $16x = \frac{1}{20}$ Putting it in eqn(i), we get : => $\frac{1}{20} + 12y = \frac{1}{8}$ => $12y = \frac{1}{8} - \frac{1}{20} = \frac{3}{40}$ => $y = \frac{3}{40 \times 12} = \frac{1}{160}$ Thus, 16 women can complete the work in = $16 \times \frac{1}{160} = \frac{1}{10}$ $\therefore$ 16 women can complete the work in 10 days.

Sixteen men and twelve women can complete a work in 8 days, if 20 men can complete the same work in 16 days, in how many days 16 women can complete the same piece of work ?1). 122). 83). 104). 15

Answer»

Solution

Let work done by 1 man be $X$ and 1 woman be $y$

Now, 16 men and 12 women complete work in 8 days.

=> $16X + 12y = \FRAC{1}{8}$ ---------Eqn(i)

Also, $20x = \frac{1}{16}$

=> $16x = \frac{1}{20}$

Putting it in eqn(i), we get :

=> $\frac{1}{20} + 12y = \frac{1}{8}$

=> $12y = \frac{1}{8} - \frac{1}{20} = \frac{3}{40}$

=> $y = \frac{3}{40 \times 12} = \frac{1}{160}$

Thus, 16 women can complete the work in = $16 \times \frac{1}{160} = \frac{1}{10}$

$\therefore$ 16 women can complete the work in 10 days.