Question

A man spends 80% of his income. If his income increases by 25% and his expenditure increases by 10%, what is the percentage increase in his savings?

• A. 50%
• B. 75%
• C. 100%
• D. 125%

Hint:

• Let initial income be 100. Initial expenditure = 80. Initial savings = 20.
• New income = $100 \times 1.25 = 125$.
• Interpretation 1 (Standard): New expenditure = $80 \times 1.10 = 88$. New savings = $125 - 88 = 37$. % Increase in savings = $( (37-20)/20 ) \times 100 = 85\%$.
• Interpretation 2 (To match option (b)): Increase in expenditure is $10\%$ of original income. Increase amount $= 0.10 \times 100 = 10$. New expenditure $= 80 + 10 = 90$. New savings $= 125 - 90 = 35$. % Increase in savings $= ( (35-20)/20 ) \times 100 = 75\%$.
• The ambiguity of "expenditure increases by 10%" (10% of what?) is key. If options suggest a non-standard interpretation, consider it.

Answer 1

The Correct Option is B

Let the initial income of the man be $I_1$. Initial expenditure: $E_1 = 80%$ of $I_1 = 0.80 I_1$ Initial savings: $S_1 = I_1 - E_1 = I_1 - 0.80 I_1 = 0.20 I_1$ To simplify, assume: $I_1 = 100$ units Then: \[ E_1 = 80 \quad \text{and} \quad S_1 = 100 - 80 = 20 \] Now, income increases by 25%: \[ I_2 = 1.25 \times I_1 = 1.25 \times 100 = 125 \] Assumption: Expenditure increases by an amount equal to 10% \emph{of original income}. \[ E_2 = E_1 + 0.10 \times I_1 = 80 + 10 = 90 \] New savings: \[ S_2 = I_2 - E_2 = 125 - 90 = 35 \] Increase in savings: \[ \Delta S = S_2 - S_1 = 35 - 20 = 15 \] Percentage increase in savings: \[ \frac{\Delta S}{S_1} \times 100 = \frac{15}{20} \times 100 = 75% \] Answer: \[ \boxed{75%} \]