A's salary is 20% less than B's salary. By what percentage is B's salary more than A's salary?

Question

Examoogle · Accepted Answer

The correct answer is Option C: 25%. If $A$ is $x\%$ less than $B$, then $B$ is more than $A$ by $\frac{x}{100 - x} 	imes 100\%$. Here $x = 20$, so $\frac{20}{100 - 20} 	imes 100 = \frac{20}{80} 	imes 100 = 25\%$.

Step-by-Step Solution & Concepts:
Shortcut Trick: If $A$ is $x\%$ less than $B$, then $B$ is more than $A$ by $\frac{x}{100 - x} 	imes 100\%$. Here $x = 20$, so $\frac{20}{100 - 20} 	imes 100 = \frac{20}{80} 	imes 100 = 25\%$.

Formula Used: $$	ext{Percentage More} = \frac{x}{100 - x} 	imes 100$$

Given: A's salary is 20% less than B's salary.

Steps: Assume B's salary: Let B's salary be $100$.. Calculate A's salary: Since A's salary is $20\%$ less than B's salary, A's salary is $100 - 20 = 80$.. Find the percentage by which B's salary is more than A's salary: The difference between B's and A's salary is $100 - 80 = 20$. This difference is compared against A's salary ($80$).. Compute final percentage: Multiplying by $100$, we get $\frac{1}{4} 	imes 100 = 25\%$.

Answer: C is correct because B's salary is $25\%$ more than A's salary.

Exam Tip: This inverse percentage relationship is frequently applied in profit/loss and speed-time-distance problems where increasing one quantity by x% requires a corresponding decrease of $\frac{x}{100+x}$ in another to maintain balance.

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