Question

The salaries of A and B are in a ratio of 2 : 3. Their savings are equal. If A's expenditure is 1/2 of the salary, then what per cent of income does B spends?

• A. 66.67 %
• B. 78.5 %
• C. 50 %
• D. 75 %

Answer 1

Answer:

A. 66.67 %

Assuming A's expenditure is $\frac{1}{2}$ of their salary:

1. Set up the salaries:

   Let the salary of A be $2x$ and the salary of B be $3x$ based on the given ratio of $2 : 3$.

2. Calculate A's expenditure and savings:

   
   $\text{A's Expenditure} = \frac{1}{2} \times 2x = x$

   $\text{A's Savings} = \text{A's Salary} - \text{A's Expenditure} = 2x - x = x$

3. Determine B's savings and expenditure:

   Since A and B have equal savings:

   
   $\text{B's Savings} = x$

   $\text{B's Expenditure} = \text{B's Salary} - \text{B's Savings} = 3x - x = 2x$

4. Calculate the percentage of income B spends:

   
   

   $\text{Percentage spent by B} = \left(\frac{\text{B's Expenditure}}{\text{B's Salary}}\right) \times 100 = \left(\frac{2x}{3x}\right) \times 100 = 66.67\% \quad \left(\text{or } 66\frac{2}{3}\%\right)$

B spends $66.67\%$ (or $66\frac{2}{3}\%$) of their income.