Question

The incomes of Rajesh and Mahesh are in the ratio 7:9 and their savings are in the ratio 5:7. What is the ratio of their expenditures in the same order, if Mahesh saves two third of his income?

Tell me its gonna eat my head

Answer 1

Answer: 19:21

Step-by-step explanation:

The ratio of incomes of rajesh and mahesh is 7:9

∴ Let their incomes be 7x and 9x

The ratio of their savings is 5:7

∴ Let their savings be 5y and 7y

Mahesh saves $\frac{2}{3}$ of his income

⇒  7y = $\frac{2}{3}$ X 9x

⇒ 7y = 6x

⇒ y = $\frac{6x}{7}$      ..... 1

expenses = income - savings

The expenses of rajesh = 7x - 5y and of mahesh =  9x - 7y

replacing the value of y from equation 1

income of rajesh = 7x - 5 X $\frac{6x}{7}$ = 7x - $\frac{30x}{7}$ = $\frac{19x}{7}$

and income of mahesh = 9x - 7 X $\frac{6x}{7}$ = 9x - 6x = 3x

ratio of the two expenses = $\frac{\frac{19x}{7} }{3x}$ = $\frac{19}{21}$

Hence the ratio of their expenses is 19:21