Question

The salaries of A, B and C together amount to Rs. 333, and they spend $80\%$, $85\%$ and $75\%$ of their respective salaries. If their savings are in the ratio 7 : 6 : 9, then their respective salaries in rupees are

• A. Rs. 102, Rs. 118 Rs. 113
• B. Rs. 105, Rs. 120 Rs. 108
• C. Rs. 85, Rs. 125 Rs. 123
• D. None of these

Answer 1

The correct option is B Rs. 105, Rs. 120 Rs. 108

Let salaries of $A,B,$ and $C$ be Rs. $x,y,$ and $z$ respectively.
Together, their amount $x+y+z=333.$
Now,
Expenditure of $A=80\%$
$\Rightarrow$ Savings $=20\%$
Expenditure of $B=85\%$
$\Rightarrow$ Savings $=15\%$
Expenditure of $C=75\%$
$\Rightarrow$ Savings $=25\%$

$\therefore$ Savings of $A=\frac{20x}{100},B=\frac{15y}{100},$ and $C=\frac{25z}{100}$
Also, given savings are in the ratio $7:6:9$
$\therefore \frac{20x}{700}=\frac{15y}{600}=\frac{25z}{900}$
$\Rightarrow \frac{20x}{7}=\frac{15y}{6}=\frac{25z}{9}$

Now, $\frac{20x}{7}=\frac{15y}{6}\Rightarrow 8x=7y=x=\frac{7y}{8}$
And $\frac{15y}{6}=\frac{25z}{9}\Rightarrow \frac{9y}{10}=z$

Given, $x+y+z=333$
$\Rightarrow \frac{7}{8}y+y+\frac{9}{10}y=333$
$\Rightarrow 222y=333\times 80$
$\Rightarrow y=120$
$\therefore x=\frac{7}{8}\left(120\right)=105,z=\frac{9}{10}\left(120\right)=108$
Hence, salary of $A=Rs.105,B=Rs.120,$ and $C=Rs.108.$