Question : P's income is 250 percent of Q's income and P's expenditure is 180 percent of Q's expenditure. If P's income is 400 percent of Q's expenditure, then what is the respective ratio of P's savings and Q's savings?
Option 1: 11 : 5
Option 2: 5 : 2
Option 3: 11 : 3
Option 4: 8 : 3
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Correct Answer: 11 : 3
Solution :
Let Q's expenditure be $x$.
⇒ P's expenditure = 180% of $x=\frac{180}{100}x=1.8x$
And, P's income = 400% of $x=4x$
⇒ P's savings = $4x - 1.8x=2.2x$
Now, P's income = 250% of Q income
⇒ 250% of Q income = $4x$
⇒ Q income = $\frac{4x}{250\%}=\frac{4x}{250}\times100=1.6x$
$\therefore$ Q's savings = $1.6x - x=0.6x$
⇒ The ratio of the savings of P and Q = $2.2x : 0.6x=11 : 3$
Hence, the correct answer is 11 : 3.
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