Question

$A,B$ and $C$ spend $70\%,75\%$ and $80\%$ respectively of their salaries. Their actual savings are in the ratio $4:5:6$. What is the ratio of their salaries?

• A. $4:5:6$
• B. $4:6:9$
• C. $6:5:4$
• D. $9:6:4$

Answer 1

The correct option is B $4:6:9$

We take their incomes as $x,y$ and $z$.

The expenses of $A=70\%$,

i.e The savings of $A=(100-70)\%=30\%=\frac{30x}{100},$

The expenses of $B=75\%$,

i.e The savings of $B=(100-75)\%=25\%=\frac{25y}{100},$

The expenses of $C$ $=80\%$,

i.e The savings of $C$ $=(100-80)\%=20\%=\frac{20z}{100}.$

By the given condition, we get

$\frac{30x}{100}$:$\frac{25y}{100}$:$\frac{20z}{100}$ $=4:5:6$.

$\Rightarrow \frac{30x}{100}=4\Rightarrow x=\frac{40}{3},\Rightarrow \frac{25y}{100}=5\Rightarrow y=20\Rightarrow \frac{20x}{100}=6\Rightarrow z=30.$

Therefore $x:y:z=\frac{40}{3}:20:30=4:6:9.$