Two numbers are 25% and 40% less than a third number respectively. By what percentage should the second number be increased so that it becomes equal to the first number?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 25%
Take the third number as 100; then both numbers are known, and the increase is worked out on the second number.
First number \(=100-25=75\); second number \(=100-40=60\)
Increase needed \(=75-60=15\)
Percentage \(\displaystyle =\frac{15}{60}\times100=25\%\)
The second number must be increased by 25%.
Why the other options are incorrect
Option (2) 15% — Incorrect. This is the gap between 40% and 25%; it must be compared with the second number, 60, not with the third.
Option (3) 60% — Incorrect. This compares the two percentages themselves, not the two numbers.
Option (4) 20% — Incorrect. This divides the gap by the first number, 75; the increase is on the second number, 60.