Radha and Vatsal invested ₹36,000 and ₹42,000, respectively, in a business. Radha, being an active partner, got ₹637.50 extra every month for running the business. In 3 years, if Radha received a total of ₹31,500, then what was the profit earned by Vatsal during this period?

Correct option is A

Given:
Radha's Investment (R): ₹36,000
Vatsal's Investment (V): ₹42,000
Radha's Extra Monthly Earnings (for managing the business): ₹637.50
Total Earnings for Radha (over 3 years): ₹31,500
Duration: 3 years
Solution:
First, compute the total extra amount Radha received over 3 years:
​$$\text{Extra Amount} = ₹637.50 \times 12 \text{ months} \times 3 \text{ years} = ₹22,950$$​
Profit Share (Radha) = ₹31,500 - ₹22,950 = ₹8,550
The investments of Radha and Vatsal are in the ratio:
Investment Ratio = 36,000 : 42,000 = 6 : 7
Let the total profit be P .
Radha's profit share is based on the investment ratio:
Radha's Share = $$\frac{6}{6 + 7} \times P = \frac{6}{13}P$$​​
We already found Radha's profit share to be ₹8,550:
​$$\frac{6}{13}P = ₹8,550$$​

​$$P = ₹8,550 \times \frac{13}{6} = ₹18,525$$​​
Using the investment ratio:
Vatsal's Share = $$\frac{7}{13} \times ₹18,525 = ₹9,975$$​​
Vatsal earned a profit of ₹9,975 over the 3-year period.