Question

Pooja and Ritu can do a piece of work in $17\frac{1}{7}$ days. If one day work of Pooja be three fourth of one day work of Ritu; find in how many days each alone will do the work.

Answer 1

Let Puja complete the work in x x $x$ days.

Work done by Puja in one day $=\frac{1}{x}$

Again, let Ritu complete the entire work alone in y y$y$ days.

Work done by Puja in one day $=\frac{1}{y}$

We also know that both Ritu and Puja complete the entire work together in $17\frac{1}{7}$ days.

$=\frac{120}{7}$ days

Work done by Puja and Ritu in one day $=\frac{1}{\frac{120}{7}}=\frac{7}{120}$

i.e.,

$\frac{1}{x}+\frac{1}{y}=\frac{7}{120}$ ---(1)

It is given that, one day work of Pooja be three fourth of one day work of Ritu.

$\Rightarrow y=\frac{3}{4}x$

$\Rightarrow \frac{1}{y}=\frac{4}{3x}$ --(2)

from (1),

$\frac{1}{x}+\frac{1}{y}=\frac{7}{120}$

$\Rightarrow \frac{1}{x}+\frac{4}{3x}=\frac{7}{120}$

$\Rightarrow \frac{3+4}{3x}=\frac{7}{120}$

$\Rightarrow \frac{7}{3x}=\frac{7}{120}$

$\Rightarrow 3x=120$

$\Rightarrow x=\frac{120}{3}$

$\Rightarrow x=40$ --(3)

and, $y=\frac{3}{4}x$

$y=\frac{3}{4}\times 40$

$\Rightarrow y=30$ ---(4)

Pooja will complete the work in $40$ days and Ritu will complete the work in $30$ days.