cat 2024 Question 22

Question

After two successive increments, Gopal's salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was

Accepted Answer

We are told that there was two successive increments in the salary, with the second increment percentage twice the first one. Total Increment was 187.5%.

Drawing up the equation

$\left(1+z\right)\left(1+2z\right)=1.875$

$1+3z+2z^2=1.875$

$2z^2+3z-0.875$

$z=\frac{\left(-3\pm\sqrt{9+8\left(0.875\right)}\right)}{4}$

$z=\frac{\left(-3\pm\ 4\right)}{4}$

$z=0.25$

Answer is 25%.

Question 22.

Question Explanation