Multiple choice

After selling a watch, Mihir found that he had made a loss of 12 %. He also found that had he sold it for Rs. 45 more, he would have made a profit of 8 %. The actual initial loss was what percentage of the profit earned, had he sold the watch for 8 % profit?

  1. 120%

  2. 110%

  3. 150%

  4. 135%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP be the cost price. Loss of 12% means SP1 = 0.88*CP. Profit of 8% means SP2 = 1.08*CP. The difference is 0.20*CP = 45, so CP = 225. The initial loss was 0.12 * 225 = 27. The profit at 8% is 0.08 * 225 = 18. The ratio 27/18 = 1.5, which is 150%.

AI explanation

Let the cost price be CP; the difference between an 8% profit and a 12% loss is represented by the equation (CP x 1.08) - (CP x 0.88) = 45. Solving this gives 0.20CP = 45, so the cost price is 45 / 0.20 = Rs. 225. The actual initial loss is 12% of 225, which is 27, and the profit from an 8% increase is 8% of 225, which is 18; finding what percentage 27 is of 18 gives (27 / 18) x 100 = 150%.

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