Question

The incomes of A, B and C are in the ratio 7 : 9 : 12 and their spendings are in the ratio 8 : 9 : 15. If A saves ${\left(1/4\right)}^{th}$ of his income then?

• A. $56:99:69$
• B. $69:56:99$
• C. $99:56:69$
• D. $99:69:56$

Answer 1

The correct option is A $56:99:69$

Solution:

Let income of $A=7x$

Income of $B=9x$

Income of $C=12x$

and Spendings of $A=8y$

Spendings of $B=9y$

Spendings of $C=15y$

Income=Savings + Expenditures

Savings of $A=\frac{1}{4}\times 7x=\frac{7x}{4}$

or, $7x=\frac{7x}{4}+8y$

or, $21x=32y$

or, $x=\frac{32}{21}y$

Now,

Income of $A=7x=7\times \frac{32}{21}y=\frac{32}{3}y$

Income of $B=9x=9\times \frac{32}{21}y=\frac{96}{7}y$

Income of $C=7x=12\times \frac{32}{21}y=\frac{128}{7}y$

Now,

Savings of $A=7x-8y=\frac{32}{3}y-8y=\frac{8}{3}y$

Savings of $B=9x-9y=\frac{96}{7}y-9y=\frac{33}{7}y$

Savings of $C=12x-15y=\frac{128}{7}y-15y=\frac{23}{7}y$

So, Savings of $A,B$ and $C$ in ratio

$\frac{8}{3}:\frac{33}{7}:\frac{23}{7}::56:99:69$

Hence, A is the correct option.