The monthly pocket money of Ravi and Sanjeev are in the ratio 5 : 7. Their expenditures are in the ratio 3 : 5. If each saves ₹80 every month, find their monthly pocket money.

Pocket money ratio of Ravi and Sanjeev = 5 : 7, so let the pocket money be 5x and 7x.

Expenditure ratio of Ravi and Sanjeev = 3 : 5, so let the expenditure be 3y and 5y.

Given, each save ₹80 per month.

∴ For Ravi, savings = 5x - 3y = 80 and for Sanjeev, savings = 7x - 5y = 80.

First solving 5x - 3y = 80.

$\Rightarrow 5x - 3y = 80 \\[0.5em] \Rightarrow 5x = 80 + 3y \\[0.5em] x = \dfrac{80 + 3y}{5}$

Putting above value of x in 7x - 5y = 80.

$\Rightarrow 7\big(\dfrac{80 + 3y}{5}\big) - 5y = 80 \\[1em] \Rightarrow \dfrac{560 + 21y}{5} - 5y = 80 \\[1em] \Rightarrow \dfrac{560 + 21y - 25y}{5} = 80 \\[1em] \Rightarrow \dfrac{560 - 4y}{5} = 80$

On cross multiplying,

$\Rightarrow 560 - 4y = 400 \\[1em] \Rightarrow 560 - 400 = 4y \\[1em] \Rightarrow 4y = 160 \\[1em] y = 40.$

∴ y = 40, x = $\dfrac{80 + 3y}{5} = \dfrac{80 + 3 \times 40}{5} = \dfrac{200}{5} = 40$

∴ 5x = 200, 7x = 280.

Hence, the pocket money of Ravi and Sanjeev is ₹200 and ₹280 respectively.