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Salary Hike Comparison

XAT 2019 · Quantitative Ability & Data Interpretation · Hard · Arithmetic

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

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

  1. A.

    E

  2. B.

    D

  3. C.

    C

  4. D.

    A

  5. E.

    E

Answer

A

Explanation

Let initial salary of an employee be S0S_0. Final salary S=S0(1+x1100)(1+x2100)S = S_0 \left(1 + \frac{x_1}{100}\right)\left(1 + \frac{x_2}{100}\right). For two percentages p+ap+a and p−a+1p-a+1, the product is proportional to (100+p+a)(100+p−a+1)=(100+p)2+(100+p)−a(a−1)(100+p+a)(100+p-a+1) = (100+p)^2 + (100+p) - a(a-1). As aa increases from AA to EE, a(a−1)a(a-1) increases, so the multiplier decreases. Thus EE has the smallest multiplier, meaning EE must have had the highest initial salary to reach the same final salary. Consequently, EE received the least net percentage hike.

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