Two numbers are 90% and 75% less than a third number respectively. By what percentage should the first number be increased so that it becomes equal to the second number?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 150%
Taking the third number as 100 gives both numbers directly. The increase is then measured on the first number, the one being increased.
First number \(=100-90=10\); second number \(=100-75=25\)
Increase needed \(=25-10=15\)
Percentage increase \(\displaystyle =\frac{15}{10}\times100=150\%\)
The first number must be increased by 150%.
Why the other options are incorrect
Option (1) 250% — Incorrect. This is the second number as a percentage of the first (\(\frac{25}{10}\times100\)), not the increase.
Option (2) 200% — Incorrect. A 200% increase makes 10 into 30, not 25.
Option (4) 100% — Incorrect. A 100% increase only doubles 10 to 20, not 25.