A trader makes a loss of 15% when selling an article. Find the ratio, selling price : cost price
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:
- Assume the Cost Price (C.P.) of the article is N100 (for simplicity).
- Apply the formula with the given Loss%: \[ \text{S.P.} = 100 - \left( 100 \times \frac{15}{100} \right) \]
- 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.
- 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:
- Given C.P. = 100 and calculated S.P. = 85.
- The ratio is \(\text{S.P.} : \text{C.P.} = 85 : 100\).
- To simplify the ratio:- Divide both parts of the ratio by their Greatest Common Divisor (GCD), which is 5.- Thus, the simplified ratio becomes \(\frac{85}{5}: \frac{100}{5} = 17: 20\).
- Conclusion:∴ The ratio of Selling Price to cost price is 17: 20.
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