Question

The income of A is \( \frac{2}{3} \) of B’s income and the expenditure of A is \( \frac{3}{4} \) of B’s expenditure. If one-third income of B is equal to the expenditure of A, then the ratio of savings of A and B will be:

• A. 3 : 5
• B. 5 : 4
• C. 3 : 2
• D. 6 : 5

Hint:

To solve such ratio-based problems, express all variables in terms of a common quantity and simplify step by step.

Answer 1

The Correct Option is A

Let the income of A be \( I$_$A \) and the income of B be \( I$_$B \). According to the question: \[ I_A = \frac{2}{3} I$_$B \] Let the expenditure of A be \( E$_$A \) and the expenditure of B be \( E$_$B \). We are given: \[ E$_$A = \frac{3}{4} E$_$B \] Additionally, we know that one-third of income of B is equal to the expenditure of A, i.e., \[ \frac{1}{3} I$_$B = E$_$A \] Substitute the value of \( E$_$A \): \[ \frac{1}{3} I$_$B = \frac{3}{4} E$_$B \] From this, calculate the ratio of savings of A and B using their respective incomes and expenditures. The final ratio of savings will be \( 3 : 5 \).