8 men can finish a piece of work in 21 days. 14 men started working and after 3 days were replaced by 9 women. These 9 women finished the remaining work in 24 days. In how many days 9 women can finish the whole work ?

Let efficiency of 1 man = $$x$$ units/day

Efficiency of 1 woman = $$y$$ units/day

Since, 8 men finish the work in 21 days

Let total work = $$x \times 8 \times 21 = 168x$$ units

Initially, 14 men worked for 3 days

=> worked completed = $$x \times 14 \times 3 = 42x$$ units

Work left = $$168x - 42x = 126x$$ units ---------------------(i)

Now, 9 women complete this work in 24 days

=> work done by women = $$y \times 9 \times 24 = 216y$$ units --------(iI)

From eqn (i) & (ii), we get : $$126x = 216y$$

=> $$\frac{x}{y} = \frac{216}{126} = \frac{12}{7}$$

$$\therefore$$ Number of days taken by 9 women to finish the work

= $$\frac{168x}{9y} = \frac{168}{9} \times \frac{12}{7}$$

= $$24 \times \frac{4}{3} = 32$$ days