Multiple choice

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. 20

  2. 25

  3. 27.5

  4. 30
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B Correct answer
Explanation

Let the first increment be x%. The second is 2x%. (1 + x/100)(1 + 2x/100) = 1.875. Let y = x/100. (1+y)(1+2y) = 1.875. 1 + 3y + 2y^2 = 1.875. 2y^2 + 3y - 0.875 = 0. Using the quadratic formula, y = 0.25. So x = 25%.

AI explanation

Using the successive percentage change formula, the final salary is 187.5% of the initial salary, meaning the total increase factor is 1.875. Let the first increment be r%, so the second increment is 2r%, which gives the equation (1 + r/100)(1 + 2r/100) = 1.875. Solving this quadratic equation yields r = 25. The percentage of salary increase in the first increment was 25.

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