The incomes of P and Q are in the ratio 7 : 3 and their expenditures are in the ratio 4 : 1. If each of them saves Rs 7500, what is the sum of their incomes?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 45000
Savings \(=\) income \(-\) expenditure. Take one unknown for the incomes and another for the expenditures; the two equal savings give two equations.
Incomes: Rs \(7k\) and Rs \(3k\); expenditures: Rs \(4m\) and Rs \(m\)
P: \(7k-4m=7500\)
Q: \(3k-m=7500\), so \(m=3k-7500\)
Putting this into P's equation: \(7k-12k+30000=7500\)
\(5k=22500\), so \(k=4500\)
Incomes \(=7\times4500=\) Rs 31500 and \(3\times4500=\) Rs 13500
Sum of incomes \(=31500+13500=\) Rs 45000
The sum of their incomes is Rs 45000.