Question : The ratio of incomes of $\mathrm{P}$ and $\mathrm{Q}$ is $1: 2$. Ratio of income of $\mathrm{Q}$ and $\mathrm{R}$ is $3: 2$. If one-third of $\mathrm{P}$ 's income is INR 4400 less than half of P's income, then what is Q's income?
Option 1: INR 56600
Option 2: INR 52800
Option 3: INR 46600
Option 4: INR 41200
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Correct Answer: INR 52800
Solution :
Given:
The ratio of incomes of P and Q is 1: 2
The ratio of income of Q and R is 3: 2
P's income = $x$
Q's income = $2x $
According to the given information:
One-third of P's income is INR 4400 less than half of P's income.
⇒ $(\frac{1}{3})x = (\frac{1}{2})× x - 4400$
⇒ $2x = 3x - 26400$
⇒ $3x – 2x = 26400$
⇒ $x = 26400$
So Q's income = $2x$ = 2 × 26400 = INR 52800
Hence, the correct answer is INR 52800.
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