The ratio of a man’s expenditure to his saving is 4 : 1. His income increases by 20% and his saving increases by 10%. By what percentage does his expenditure increase?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 22.5%
Income \(=\) expenditure \(+\) saving. Take the old values in the given ratio, find the new income and new saving, and the new expenditure is the difference.
Old: expenditure 4, saving 1, income 5
New income \(=5\times1.2=6\); new saving \(=1\times1.1=1.1\)
New expenditure \(=6-1.1=4.9\)
Increase \(\displaystyle =\frac{4.9-4}{4}\times100=22.5\%\)
His expenditure increases by 22.5%.
Why the other options are incorrect
Option (1) 10% — Incorrect. This subtracts the two percentages; they are on different amounts (income and saving).
Option (3) 18% — Incorrect. This works out the rise in expenditure as a percentage of the old income, not of the old expenditure.
Option (4) 20% — Incorrect. This assumes expenditure rises in the same proportion as income; saving rises by less, so expenditure must rise by more.