CAT 2024 Slot 3 QA Question & Solution
ArithmeticEasy
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
Options
30
27.5
25
20
Solution
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%.