XAT 2015 QA Question 14 · Algebra - Inequalities & Modulus

Let a + b + c = X

We need to find the maximum value of:

$\frac{X+d}{X-d}=\frac{(X-d)+2d}{X-d}=1+\frac{2d}{X-d}$

$$\begin{gathered} \frac{}{} \\ \frac{2d}{X-d} \end{gathered}$$

$\frac{\mathrm{is\; maximum\; when\; d\; is\; maximum}}{}$ and X is minimum possible.

∴ d = 25 and X = 26
The highest possible value of the given expression = 1 + (2 × 25) = 51
Hence, option (c).