Prashanth sold an album for $735 and made a profit of 22.5%. The cost price of…

2024

Prashanth sold an album for $735 and made a profit of 22.5%. The cost price of the album went up by $120, so Prashanth increased the selling price by $120 as well. What is his profit percentage now?

  1. A.

    20

  2. B.

    25

  3. C.

    18.75

  4. D.

    2.25

Show answer & explanation

Correct answer: C

Profit percentage is always calculated on the Cost Price (CP): Profit% = (SP − CP) / CP × 100. Equivalently, CP = SP × 100 / (100 + Profit%). This lets us recover the cost price when the selling price and profit percentage are known, and the formula must be reapplied with FRESH cost and selling price figures whenever either one changes.

  1. Find the original cost price from the given selling price and profit percentage: CP = 735 × 100/122.5 = Rs. 600.

  2. Add the $120 rise to the cost price: New CP = 600 + 120 = Rs. 720.

  3. Add the same $120 rise to the selling price, as stated: New SP = 735 + 120 = Rs. 855.

  4. Find the new profit in rupees: New Profit = New SP − New CP = 855 − 720 = Rs. 135.

  5. Apply the profit-percentage formula again, using the NEW cost price as the base: New Profit% = (135/720) × 100 = 18.75%.

Cross-check: New SP ÷ New CP = 855/720 = 1.1875, i.e. 18.75% above cost — consistent with the profit computed above, confirming the result.

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