CAT 2024 Slot 3 QA Question 20: 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

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

Accepted Answer

Let the first percentage increase be $x\%$. Then the second percentage increase is $2x\%$.

$(1 + \dfrac{x}{100})(1 + \dfrac{2x}{100}) = 187.5\% = \dfrac{15}{8}$

Put $r = \dfrac{x}{100}$.

$(1 + r)(1 + 2r) = \dfrac{15}{8}$
$1 + 3r + 2r^{2} = \dfrac{15}{8}$
$16r^{2} + 24r - 7 = 0$
$(4r - 1)(4r + 7)

After two successive increments, Gopal’s salary became 187.5%187.5\%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

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