Question

An item with a cost price of Rs.1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on the cost price. If the discount was doubled, the profit would have been Rs.110. The rate of discount, in percentage, at which the profit percentage would be equal to the rate of discount, is nearest to:

• A. \(12\)
• B. \(13\)
• C. \(14\)
• D. \(15\)

Hint:

When the same marked price is used under different discount and profit conditions, set up equations using \(SP = MP - \text{Discount}\) and \(SP = CP + \text{Profit}\) for each scenario. Once the marked price is known, you can introduce a variable discount rate and equate the profit percentage to that rate to solve such “rate equals rate” problems.

Answer 1

The Correct Option is C

Approach: Once you have the marked price (Rs 2200) and cost (Rs 1650), reframe the last condition as a ratio. Discount% acts on MP, profit% acts on CP, and they must be equal — so compare what one rupee of percentage buys on each side.

Step 1: Pin down $MP$. With $20\%$ profit, $SP_1 = 1.2 \times 1650 = 1980$. Doubling the discount drops profit to Rs $110$, i.e. $SP_2 = 1760$. The extra discount $D$ caused a drop of $1980 - 1760 = 220$, so $D = 220$ and $MP = 1980 + 220 = 2200$.

Step 2: Let the equal rate be $x\%$. Reading $SP$ two ways: from the marked side $SP = MP(1 - x/100) = 2200 - 22x$; from the cost side $SP = CP(1 + x/100) = 1650 + 16.5x$.

Step 3: Set the two expressions for $SP$ equal: \[ 2200 - 22x = 1650 + 16.5x. \] So $2200 - 1650 = 22x + 16.5x$, giving $550 = 38.5x$ and \[ x = \frac{550}{38.5} = \frac{100}{7} \approx 14.29. \]

Step 4: The nearest whole number is $14$.

Final answer: $14$ — option 3.