Multiple choice

The profit made when a shopkeeper increases his selling price by 20% and sells eight items is the same as the loss made when he decreases his selling price by 20% and sells nine items. Find the ratio of the original cost price to the selling price of each item.

  1. 80 120

  2. 64 144

  3. 168 170

  4. 170 168
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = C, SP = S. Profit = 8*(1.2S - C) = Loss = 9*(C - 0.8S). 9.6S - 8C = 9C - 7.2S. 16.8S = 17C. C/S = 16.8/17 = 168/170.

AI explanation

Let the cost price be C and original selling price be S. Profit at 8 items is 8(1.2S - C) and loss at 9 items is 9(C - 0.8S). Equating the magnitudes gives 9.6S - 8C = 9C - 7.2S. Solving yields 16.8S = 17C, making the ratio of cost price to selling price 168 to 170.

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