A trader makes a loss of 15% when selling an article. Find the ratio, selling price : cost price

  • A 3:20
  • B 3:17
  • C 17:20
  • D 20:23

The correct answer is C. 17:20

Given Data:

  • Loss Percentage (Loss%) = 15%

To find the Selling Price (S.P.), we use the formula:

\[ \text{S.P.} = \text{C.P.} - \left( \text{C.P.} \times \frac{\text{Loss%}}{100} \right) \]

Calculation Steps:

  1. Assume the Cost Price (C.P.) of the article is N100 (for simplicity).
  2. Apply the formula with the given Loss%:   \[ \text{S.P.} = 100 - \left( 100 \times \frac{15}{100} \right) \]
  3. Calculate the reduction due to loss:   \[ \text{S.P.} = 100 - 15 \]   The N15 is the monetary value of the 15% loss on the C.P.
  4. Therefore, the Selling Price after accounting for the loss:   \[ \text{S.P.} = 85 \]

Now, let's find the ratio of the selling price to the Cost price:

  1. Given C.P. = 100 and calculated S.P. = 85.
  2. The ratio is \(\text{S.P.} : \text{C.P.} = 85 : 100\).
  3. To simplify the ratio:- Divide both parts of the ratio by their Greatest Common Divisor (GCD), which is 5.- Thus, the simplified ratio becomes \(\frac{85}{5}: \frac{100}{5} = 17: 20\).
  4. Conclusion:∴ The ratio of Selling Price to cost price is 17: 20.
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