Multiple choice

A shopkeeper sold one fourth of his goods at a loss of $10\%$. He sold the remaining at a higher percent of profit to get $\displaystyle 12\frac{1}{2}$% profit on the whole transaction. The higher profit percent is

  1. $\displaystyle 17\frac{1}{2}$%
  2. $\displaystyle 33\frac{1}{3}$%
  3. $\displaystyle 22\frac{1}{2}$%
  4. $20\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the total goods be 1 unit. 1/4 sold at 10% loss (-0.1 * 1/4 = -0.025). Remaining 3/4 sold at x% profit. Total profit required = 12.5% (0.125). Equation: -0.025 + 0.75x = 0.125. 0.75x = 0.15. x = 0.15 / 0.75 = 0.2 = 20%.

AI explanation

Assume the total cost price of the goods is Rs. 400, so one fourth costs Rs. 100 and the remaining three fourths cost Rs. 300. The target profit of 12.5% on the whole means a total selling price of Rs. 450, and the first quarter sells at a 10% loss for Rs. 90. This leaves Rs. 360 to be recovered from the remaining goods costing Rs. 300, so the required profit is (360 - 300) divided by 300, which equals 20%.

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