Swati's salary is 30% more than Ajay's salary. By what approximate percentage…
2023
Swati's salary is 30% more than Ajay's salary. By what approximate percentage is Ajay's salary less than Swati's salary?
Answer: B. 23% — ConceptA percentage comparison must use the quantity named after “than” as its base. Reversing a comparison changes that base, so a 30% increase does not…
- A.
33%
- B.
23%
- C.
13%
- D.
30%
Show answer & explanation
Correct answer: B
Concept
A percentage comparison must use the quantity named after “than” as its base. Reversing a comparison changes that base, so a 30% increase does not become a 30% decrease.
If one quantity is r% more than another, the reverse percentage decrease is obtained by dividing the same absolute difference by the larger quantity and multiplying by 100.
Application
Let Ajay’s salary be 100 units.
Swati’s salary is 30% more, so it is 100 + 30 = 130 units.
The salary difference is 130 − 100 = 30 units.
Using Swati’s salary as the base, the required decrease is (30 ÷ 130) × 100 = 23.0769…%, which is approximately 23%.
Cross-check
Reducing 130 by 23% gives 130 × 0.77 = 100.1, which is approximately Ajay’s assumed salary of 100. Therefore, the required approximate percentage is 23%.