The ratio of the income of A to that of B is 3 : 7. A and B save Rs 4,000 and Rs 2,000 respectively. If the expenditure of A is equal to \(16\frac{2}{3}\)% of the expenditure of B, then the total income of A and B is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 20,000
Expenditure = income − saving. Write both expenditures from the income ratio and use \(\displaystyle 16\frac{2}{3}\%=\frac{1}{6}\).
Incomes: A \(=3x\), B \(=7x\)
Expenditures: A \(=3x-4000\), B \(=7x-2000\)
\(\displaystyle 3x-4000=\frac{1}{6}(7x-2000)\)
\(18x-24000=7x-2000\), so \(11x=22000\)
\(x=2000\)
Total income \(=3x+7x=10x=\) Rs 20,000
Check: expenditures Rs 2,000 and Rs 12,000, and \(\displaystyle \frac{2000}{12000}=\frac{1}{6}\)
The total income of A and B is Rs 20,000.