Consider the following statements:
I. If A is 25% more than B, then B is 20% less than A.
II. If A’s salary is 40% less than B’s salary, then B’s salary is 40% more than A’s salary.
III. If \(x\) is 50% of \(y\), then \(y\) is 200% of \(x\).
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → I and III only
A percentage comparison is always taken on the quantity that comes after ‘than’ (or after ‘of’); changing the base changes the percentage.
I. If A is 25% more than B, then B is 20% less than A. — Correct. B is less than A by 25 on a base of 125, which is 20%.
Take B \(=100\); then A \(=125\)
B is less than A by \(125-100=25\)
As a percentage of A: \(\displaystyle\frac{25}{125}\times100=20\%\)
II. If A’s salary is 40% less than B’s salary, then B’s salary is 40% more than A’s salary. — Incorrect. The difference is the same, but the base is now A’s smaller salary, so the percentage is \(66\frac{2}{3}\%\), not 40%.
Take B’s salary \(=100\); then A’s salary \(=60\)
B’s salary exceeds A’s by \(40\)
As a percentage of A’s salary: \(\displaystyle\frac{40}{60}\times100=66\frac{2}{3}\%\)
III. If \(x\) is 50% of \(y\), then \(y\) is 200% of \(x\). — Correct. \(y\) is twice \(x\).
\(x=0.5y\), so \(y=2x\)
\(2x=200\%\) of \(x\)