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

Working backward from the selling price to find the mixture's cost price first, then splitting that cost using the ingredient ratio, keeps this problem in clean, manageable stages.

1. Profit of $66\frac{2}{3}\%$ means selling price is $\frac{5}{3}$ of cost price (since $1+\frac{2}{3}=\frac{5}{3}$), so cost price $= 15 \div \frac{5}{3} = 9$ Rs/kg.
2. Let flour cost $3x$ and sugar cost $7x$ per kg, matching the given $3:7$ (flour:sugar) price ratio.
3. The rasgulla mix is 5 parts flour to 3 parts sugar by weight (8 parts total), so the blended cost per kg is a weighted average: $\frac{5(3x)+3(7x)}{8} = \frac{15x+21x}{8}=\frac{36x}{8}=4.5x$.
4. Setting this equal to the known cost price: $4.5x = 9 \Rightarrow x = 2$.
5. Sugar's price per kg $= 7x = 14$.

So the correct answer is option D, Rs. 14/kg.