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Marked Price and Profit Calculation

CAT 2025 Slot 3 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2025 Slot 3 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed marked price was used for the product in all the four months. Discounts of 20%, 10% and 5% were given on the marked price per unit in January, February and March, respectively, while no discounts were given in April. If the total profit from January to April was Rs. 138825, then the marked price per unit, in rupees, was

  1. A.

    520

  2. B.

    525

  3. C.

    510

  4. D.

    515

Answer

B

Explanation

Total units sold = 120+135+150+165=570120 + 135 + 150 + 165 = 570. Total Cost Price = 570×240=136,800570 \times 240 = 136,800. Let XX be the marked price. Selling prices:

  • Jan: 120×0.80X=96X120 \times 0.80X = 96X
  • Feb: 135×0.90X=121.5X135 \times 0.90X = 121.5X
  • Mar: 150×0.95X=142.5X150 \times 0.95X = 142.5X
  • Apr: 165×1.00X=165X165 \times 1.00X = 165X Total Revenue = (96+121.5+142.5+165)X=525X(96 + 121.5 + 142.5 + 165)X = 525X. Profit = Revenue - Cost Price = 525X−136,800=138,825525X - 136,800 = 138,825. 525X=275,625  ⟹  X=525525X = 275,625 \implies X = 525.

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