Question

Three person's A, B and C whose salaries together are Rs. $14400$ and expenditures are $80\%$, $85\%$ and $75\%$ of their salaries respectively. If their savings are in the ratio $8:9:20$ , then find their respective salaires.

• A. Rs.$3000$, Rs. $5000,$ Rs$.6400$
• B. Rs. $3400$, Rs. $4800$, Rs. $6200$
• C. Rs. $3200$, Rs. $4800,$ Rs. $6400$
• D. Rs. $3000$, Rs. $5200,$ Rs. $6200$

Answer 1

The correct option is C Rs. $3200$, Rs. $4800,$ Rs. $6400$

Total salaries of A, B and C = Rs. 14400
Let the salaries of A, B and C be Rs. x, Rs. y and Rs. z respectively.
$\therefore x+y+z=14400$ ......... (1)

Their spendings are 80%, 85% and 75% respectively,

$\therefore$ Their savings are 20%, 15% and 25% respectively and also their savings are given in the ratio 8 : 9 : 20

$\frac{\frac{20x}{100}}{\frac{15y}{100}}=\frac{8}{9}$ and $\frac{\frac{15y}{100}}{\frac{25z}{100}}=\frac{9}{20}$
$\Rightarrow \frac{20x}{15y}=\frac{8}{9}\Rightarrow x=\frac{8\times 15}{9\times 20}y=\frac{2}{3}y$ ...(2)

and $\frac{15y}{25z}=\frac{9}{20}\Rightarrow z=\frac{15\times 20}{9\times 25}y=\frac{4}{3}y..\left(3\right)$

$\therefore$ From eq. (1), (2), and (3) , we have
$\frac{2}{3}y+y+\frac{4}{3}y=14400\Rightarrow \frac{9y}{3}=14400\Rightarrow y=Rs.\frac{14400}{3}=Rs.4800$
$\therefore x=\frac{2}{3}\times Rs.4800=Rs.3200andz=\frac{4}{3}\times Rs.4800=Rs.6400$