Profit and Loss Question 4 - CAT 2024
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 that in the first increment, then the percentage of salary increase in the first increment was:
Step-by-Step Explanation
Let the percentage increase in the first increment be z (expressed as a fraction). The second increment is twice the first, which means it equals 2z.
The total salary after two successive increments becomes 187.5% of the initial salary, which translates to a multiplier of 1.875:
(1 + z)(1 + 2z) = 1.875
1 + 3z + 2z² = 1.875
2z² + 3z − 0.875 = 0
To eliminate decimals, multiply the entire equation by 8:
16z² + 24z − 7 = 0
Factor the quadratic equation by splitting the middle term:
16z² + 28z − 4z − 7 = 0
4z(4z + 7) − 1(4z + 7) = 0
(4z − 1)(4z + 7) = 0
Since the salary increment must be positive,
4z − 1 = 0
z = 0.25
Expressed as a percentage, the first increment is 25%.
Correct Option: C
💡 FundaMakers Tip:
When solving successive percentage problems with clear multiple-choice options, reverse engineering from the options is significantly faster than solving quadratics.
- Try Option C (25%): First increase is 25% (multiplier = 1.25). Second increase is double, which is 50% (multiplier = 1.50).
- Net multiplier = 1.25 × 1.50 = 1.875, which perfectly matches 187.5%. The answer is verified in less than 10 seconds!