Question

A, B, C, D and E are five employees working in a company. In two successive years, each of them got hikes in his salary as follows:

A : $p\%$ and $(p+1)\%$ ,
B : $(p+2)\%$ and $(p-1)\%$ ,
C : $(p+3)\%$ and $(p-2)\%$ ,
D : $(p+4)\%$ and $(p-3)\%$ ,
E : $(p+5)\%$ and $(p-4)\%$ .

If all of them have the same salary at the end of two years, who got the least hike in his salary?

Accepted Answer

A. Let initial salary of an employee be $S_0$. Final salary $S = S_0 \left(1 + \frac{x_1}{100}\right)\left(1 + \frac{x_2}{100}\right)$. For two percentages $p+a$ and $p-a+1$, the product is proportional to $(100+p+a)(100+p-a+1) = (100+p)^2 + (100+p) - a(a-1)$. As $a$ increases from $A$ to $E$, $a(a-1)$ increases, so the multiplier decreases. Thus $E$ has the smallest multiplier, meaning $E$ must have had the highest initial salary to reach the same final salary. Consequently, $E$ received the least net percentage hike.

Salary Hike Comparison

Explanation

Practise this under exam conditions