Question

Ram donated $\frac{1}{10}$ of his salary to an orphanage, $\frac{1}{3}$ of his salary spent on food, $\frac{1}{4}$ of salary on rent and electricity and $\frac{1}{20}$ of his salary on telephone. This month he donated ₹5000 in Prime Minister relief fund . He was left with ₹3000 with him, find his monthly salary.

Answer 1

Let Ram's salary be x. Then
$x=\frac{x}{10}+\frac{x}{3}+\frac{x}{4}+\frac{x}{20}+5000+3000$

where,
$\frac{x}{10}$ = amount donated to orphanage
$\frac{x}{3}$ = amount spent on food
$\frac{x}{4}$ = amount spent on rent and electricity
$\frac{x}{20}$ = amount spent on telephone
5000 = amount donated to PM Relief Fund and
3000 = balance

The LCM of $10,3,4,$ and $20$ is $60$.

Thus, x =$\frac{(6x+20x+15x+3x+300000+180000)}{60}$

or $60x=44x+480000$

$60x-44x=480000$

or $16x=480000$

x = $\frac{480000}{16}=30,000$

Thus, Ram's monthly salary is Rs. 30,000.