A man spends 60% of his income and saves the remaining. His income increases by 28% and his expenditure also increases by 30%. Find the percentage increase in his savings.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → No change
Note: The given answer is as per the official NTA Answer Key. However, none of the given options appears to be correct. With the printed figures the savings rise by 25%, which is not there in any of the options; NTA’s “No change” would follow only if the income rose by 18%, as explained below.
Savings are what is left of the income after the expenditure, so the new savings = new income − new expenditure.
Assuming the income to be 100:
Expenditure \(=60\), savings \(=100-60=40\)
New income (up 28%) \(=128\)
New expenditure (up 30%) \(=60\times1.3=78\)
New savings \(=128-78=50\)
Increase in savings \(\displaystyle=\frac{50-40}{40}\times100=25\%\)
With an income rise of 18% (which gives NTA’s answer):
New income \(=118\), new savings \(=118-78=40\), the same as before: no change