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Successive percentage salary increments

CAT 2024 Slot 3 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2024 Slot 3 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

  1. A.

    27.5

  2. B.

    30

  3. C.

    25

  4. D.

    20

Answer

C

Explanation

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

The overall increase factor is 187.5%=1.875=158187.5\% = 1.875 = \frac{15}{8}.

Setting up the equation: (1+x100)(1+2x100)=158\left(1 + \frac{x}{100}\right)\left(1 + \frac{2x}{100}\right) = \frac{15}{8}

Let y=x100y = \frac{x}{100}: (1+y)(1+2y)=158  ⟹  8(1+3y+2y2)=15(1 + y)(1 + 2y) = \frac{15}{8} \implies 8(1 + 3y + 2y^2) = 15 16y2+24y−7=016y^2 + 24y - 7 = 0 (4y+7)(4y−1)=0(4y + 7)(4y - 1) = 0

Since y>0y > 0, y=14=0.25y = \frac{1}{4} = 0.25.

Therefore, x=25%x = 25\%.

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