Out of her total monthly income, a woman spends 60% on household expenses and 15% on savings. The remaining is spent on other items. What percentage of her income is spent on these other items?
- (a)35%
- (b)25%
- (c)20%
- (d)30%
Answer
Why
Correct — B. Both given shares are percentages of the same total income, so they add, and all three shares together make 100%.
Household + savings = 60% + 15% = 75%
Other items = 100% − 75% = 25% → option (b).
Check: 60 + 15 + 25 = 100.
Why the others are wrong
- (a)35% — 35% would make the three shares 60 + 15 + 35 = 110% of her income, more than she earns. The remainder after 75% is 25%.
- (c)20% — 20% makes the shares total 60 + 15 + 20 = 95%, leaving 5% of her income unaccounted for. The remainder must close the gap to 100%.
- (d)30% — 30% gives 60 + 15 + 30 = 105% of her income, which is impossible. Household expenses and savings take 75%, so 25% is left.
Concept
When every share is quoted as a percentage of one whole, the shares add, and the missing share is 100% minus the rest.
The stem fixes the base in its first words, "Out of her total monthly income", so 60% and 15% are both taken on the full income.
The variant to watch quotes a share as a percentage of the remaining amount. Those percentages cannot be added, because each one shrinks the base before the next is applied.
Key facts
- Shares of one whole always total 100%.
- Household expenses and savings take 60% + 15% = 75% of her income.
- Other items take 100% − 75% = 25%.
Study next
Common traps
- Taking 15% of the 40% left after household expenses (6%) and ending at 34%, which misreads "Out of her total monthly income".
- Subtracting only the household share, 100 − 60 = 40%, and forgetting that savings also come out of the same income.
Every share here is a percentage of the total, so the shares add.
24 Sep 2024, 12:30, Quant Q.15 is the contrasting case: Vipul spends 30% on rent and then 60% of the remaining on groceries, so groceries take 0.7 × 0.6 = 0.42 of his income, not 60%.
Related PYQs
No directly related past PYQ was found.