Question:medium

If the selling price of an article is five times the discount offered and if the percentage of discount is equal to the percentage profit, what is the ratio of the discount offered to the cost price?

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Let profit percent equal discount percent and express selling price, marked price and discount all in terms of cost price.
Updated On: Jul 21, 2026
  • \(11:30\)
  • \(4:15\)
  • \(7:30\)
  • \(1:6\)
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The Correct Option is C

Solution and Explanation

Step 1: Assume a convenient cost price.
Let \(CP=100\) and let the common discount percent and profit percent both equal \(p\).
Then \(SP=100+p\), since a profit of \(p\%\) is added to the cost price.

Step 2: Write the marked price using the discount percent.
Since the discount is \(p\%\) of \(MP\), \(SP=MP\left(1-\dfrac{p}{100}\right)\), so \(MP=\dfrac{100+p}{1-p/100}\).

Step 3: Use the given relation \(SP=5D\).
The discount is \(D=MP-SP\), and \(SP=5D\) means \(D=\dfrac{SP}{5}=\dfrac{100+p}{5}\).

Step 4: Also express \(D\) from the marked price side and equate.
\(D=MP-SP=SP\left(\dfrac{1}{1-p/100}-1\right)=SP\times\dfrac{p}{100-p}\).
Setting the two expressions for \(D\) equal, \(\dfrac{SP}{5}=SP\times\dfrac{p}{100-p}\), so \(\dfrac{1}{5}=\dfrac{p}{100-p}\), giving \(100-p=5p\), so \(p=\dfrac{100}{6}=\dfrac{50}{3}\).

Step 5: Compute the actual numbers.
\(SP=100+\dfrac{50}{3}=\dfrac{350}{3}\), and \(D=\dfrac{SP}{5}=\dfrac{70}{3}\).

Step 6: Form the ratio.
\(D:CP=\dfrac{70}{3}:100=70:300=7:30\), which agrees with the algebraic method.

Final Answer:
Taking cost price as 100 confirms the ratio of discount to cost price is 7 is to 30. \[ \boxed{7:30} \]
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