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.

• A. Pooja in $44$ days and Ritu in $8$ days
• B. Pooja in $80$ days and Ritu in $500$ days
• C. Pooja in $20$ days and Ritu in $120$ days
• D. Pooja in $40$ days and Ritu in $30$ days

Answer 1

Answer: (D)

Let Pooja's one day work be $x$

And Ritu's one day work be $y$

Accprding to first condition,

Pooja and Ritu can do work in $17\frac{1}{7}$ days i.e $\frac{120}{7}$ days

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

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

According to second condition,

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

$\therefore 4x-3y=0$ .......... Equation $2$

Multiplying eqution $1$ by $3$ and solving equation $1$ and $2$ simultaneosly, we get

$3x+3y=\frac{7}{40}$

$4x-3y=0$

$\therefore 7x=\frac{7}{40}$

$\therefore x=\frac{1}{40}$

Putting the value of $x$ in equation $1$ , we get

$\frac{1}{40}+y=\frac{7}{120}$

$\therefore y=\frac{4}{120}=\frac{1}{30}$

$\therefore$ Pooja's one day work is $x=\frac{1}{40}$

i.e. her whole work will be completed in $40$ days

Similarly Pooja's work will be completed in $30$ days

Answer : Pooja can do the work alone in $40$ days and Ritu in $30$ days