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

C. Let the first percentage increase be $x\%$. Then the second percentage increase is $2x\%$. The overall increase factor is $187.5\% = 1.875 = \frac{15}{8}$. Setting up the equation: $$\left(1 + \frac{x}{100}\right)\left(1 + \frac{2x}{100}\right) = \frac{15}{8}$$ Let $y = \frac{x}{100}$: $$(1 + y)(1 + 2y) = \frac{15}{8} \implies 8(1 + 3y + 2y^2) = 15$$ $$16y^2 + 24y - 7 = 0$$ $$(4y + 7)(4y - 1) = 0$$ Since $y > 0$, $y = \frac{1}{4} = 0.25$. Therefore, $x = 25\%$.

Successive percentage salary increments

Explanation

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