Find the ratio of the cost price (purchase price) to the selling price if…

2024

Find the ratio of the cost price (purchase price) to the selling price if there is a loss of 12 1⁄2%.

  1. A.

    7 : 8

  2. B.

    8 : 7

  3. C.

    2 : 25

  4. D.

    25 : 2

Show answer & explanation

Correct answer: B

For any item sold at a loss, Loss% = (CP − SP)/CP × 100, where CP is the cost price and SP is the selling price. Rearranging this identity for a given loss percentage directly yields the ratio CP : SP, since SP = CP × (1 − Loss%/100).

  1. Convert the mixed percentage to a fraction: 12 1⁄2% = 25⁄2%.

  2. Substitute into the loss formula: 25⁄2 = (CP − SP)/CP × 100.

  3. Simplify the right-hand side: (CP − SP)/CP = 25⁄200 = 1⁄8.

  4. Rearrange for SP: CP − SP = CP⁄8, so SP = CP − CP⁄8 = 7CP⁄8.

  5. Form the ratio: CP/SP = CP ÷ 7CP⁄8 = 8⁄7, i.e. CP : SP = 8 : 7.

Cross-check: taking CP = 8 and SP = 7, Loss = CP − SP = 1, so Loss% = 1⁄8 × 100 = 12.5%, matching the given 12 1⁄2% loss and confirming CP : SP = 8 : 7.

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