Question

Ramsukh bhai sells rasgulla (a favourite Indian sweet) at Rs. 15 per kg. A rasgulla is made up of flour and sugar in the ratio 5 : 3 (by weight). The ratio of the price of sugar to flour is 7 : 3 (per kg). He earns a profit of \(66\dfrac{2}{3}\%\). What is the cost price of sugar?

• A. Rs. 10/kg
• B. Rs. 9/kg
• C. Rs. 18/kg
• D. Rs. 14/kg

Hint:

First find the rasgulla's own cost price from the 66⅔% profit, then split that cost using the 5:3 flour:sugar weight ratio and 3:7 price ratio.

Answer 1

The Correct Option is D

Step 1: Find the cost price per kg of rasgulla.
Selling price = Rs. 15/kg, profit \(=66\dfrac{2}{3}\%=\dfrac{200}{3}\%\). Using \(SP=CP\left(1+\dfrac{\text{profit}\%}{100}\right)\): \(15=CP\left(1+\dfrac{2}{3}\right)=CP\times\dfrac{5}{3}\), so \(CP=15\times\dfrac{3}{5}=9\) Rs/kg.

Step 2: Set up the price of sugar and flour.
Let the price of sugar be 7x and flour be 3x per kg (matching the given 7:3 ratio).

Step 3: Set up the weighted average cost.
Since flour and sugar are mixed in the ratio 5:3 by weight (5 parts flour, 3 parts sugar out of 8 total), the cost per kg of the mixture is: \(CP=\dfrac{5\times3x+3\times7x}{8}=\dfrac{15x+21x}{8}=\dfrac{36x}{8}=4.5x\).

Step 4: Solve for x.
\(4.5x=9 \Rightarrow x=2\).

Step 5: Find the cost price of sugar.
Sugar's price \(=7x=7\times2=14\) Rs/kg.

Step 6: Final Answer.
The cost price of sugar is Rs. 14/kg, so option D is correct.