**Mithu bhai sells rasgulla at Rs. 15 per kg. A rasgulla is made up of flour and sugar in the ratio of quantity 5 : 3. The ratio of price per kg of sugar and flour is 7 : 3. Thus, he earns $\frac{200}{3} \%$ profit. What is the cost price of sugar per kg?**

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Accepted Answer

**Solution:**

1. Let the cost price (CP) of rasgulla be $x$ Rs/kg.

2. Given profit percentage is $\frac{200}{3} \% = 66.66\%$.

3. Selling price (SP) = Rs. 15/kg.

4. Using profit formula:
   $$
   \text{Profit \%} = \frac{SP - CP}{CP} \times 100
   $$
   Substitute values:
   $$
   66.66 = \frac{15 - x}{x} \times 100
   $$

5. Simplify:
   $$
   \frac{15 - x}{x} = \frac{66.66}{100} = \frac{2}{3}
   $$

6. Cross multiply:
   $$
   15 - x = \frac{2}{3} x
   $$

7. Rearrange:
   $$
   15 = x + \frac{2}{3} x = \frac{5}{3} x
   $$

8. Solve for $x$:
   $$
   x = \frac{15 \times 3}{5} = 9
   $$

So, CP of rasgulla = Rs. 9/kg.

9. Rasgulla is made of flour and sugar in quantity ratio 5 : 3.

10. Let price per kg of flour = $3k$ and sugar = $7k$ (given price ratio 7 : 3 for sugar : flour).

11. Total cost price of rasgulla per kg is:
    $$
    \frac{5}{8} \times 3k + \frac{3}{8} \times 7k = 9
    $$

12. Calculate:
    $$
    \frac{15k}{8} + \frac{21k}{8} = 9 \ 
    \frac{36k}{8} = 9 \ 
    4.5k = 9 \ 
    k = 2
    $$

13. Price per kg of sugar = $7k = 7 \times 2 = 14$ Rs/kg.

**Answer:** Rs. 14/kg

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