A man purchased 20 dozen mangoes for ₹1,000. Out of these, 40 mangoes were rotten and could not be sold. At what rate per dozen should he sell the remaining mangoes to make a profit of 30%?

Correct option is A

Given:
Total mangoes purchased: 20 dozen = 240 mangoes
Cost Price (CP)= ₹1,000
Rotten mangoes= 40
Desired Profit= 30%
Formula Used:
Rate per dozen =$$\frac{\text{Total SP}}{\text{Number of dozen remaining}}$$​
Solution:

Remaining mangoes=240 - 40 = 200 mangoes$$= \frac{200}{12} = 16.\overline{6}$$ dozen

$$\text{SP} = \text{CP} + 30\% \text{ of CP} = 1000 + 300 = ₹1,300$$​​
Total Selling Price for 30% Profit:

$$\text{SP} = 1000 + \left(\frac{30}{100} \times 1000\right) = ₹1,300$$​​
Convert Remaining Mangoes to Dozens:
​$$200 \text{ mangoes} = \frac{200}{12} = 16\frac{2}{3} \text{ dozen}$$

​Rate per dozen =$$\frac{1300}{16\frac{2}{3}} = \frac{1300 \times 3}{50} = ₹78$$​