Understanding the Investment Difference Problem

This problem involves a business partnership where two individuals, Ritik and Sanjay, make a total investment. We are given the total investment amount, the total profit earned at the end of the year, and the profit share received by Sanjay. The goal is to find the difference between the amounts Ritik and Sanjay initially invested.

The core principle here is that in a business partnership, profits are typically distributed in proportion to the investments made by each partner. Therefore, the ratio of their profit shares will be the same as the ratio of their investments.

Calculating Profit Shares

First, let's determine the profit share for Ritik.

• Total Profit = ₹15,600
• Sanjay's Profit Share = ₹1,900
• Ritik's Profit Share = Total Profit - Sanjay's Profit Share
• Ritik's Profit Share = $15,600 - 1,900 = \\text{₹}13,700$

Determining the Investment Ratio

Since the profit share is proportional to the investment, we can find the ratio of their investments by looking at the ratio of their profit shares.

• Investment Ratio (Ritik : Sanjay) = Ritik's Profit Share : Sanjay's Profit Share
• Investment Ratio (Ritik : Sanjay) = $13,700 : 1,900$
• Simplifying the ratio by dividing both sides by 100: $137 : 19$

This means that for every ₹137 Ritik invested, Sanjay invested ₹19.

Calculating Individual Investments

The total investment made by both Ritik and Sanjay is ₹62,400. We can use the investment ratio to find out how much each person invested.

• Sum of the ratio parts = $137 + 19 = 156$
• Ritik's Investment = $(\\frac{\\text{Ritik's ratio part}}{\\text{Sum of ratio parts}}) \\times \\text{Total Investment}$
• Ritik's Investment = $(\\frac{137}{156}) \\times \\text{₹}62,400$
• Let's calculate the value of one ratio part: $\\frac{\\text{₹}62,400}{156} = \\text{₹}400$
• So, Ritik's Investment = $137 \\times \\text{₹}400 = \\text{₹}54,800$
• Sanjay's Investment = $(\\frac{\\text{Sanjay's ratio part}}{\\text{Sum of ratio parts}}) \\times \\text{Total Investment}$
• Sanjay's Investment = $(\\frac{19}{156}) \\times \\text{₹}62,400$
• Sanjay's Investment = $19 \\times \\text{₹}400 = \\text{₹}7,600$

We can check if the sum of their investments equals the total investment: ₹54,800 + ₹7,600 = ₹62,400. This matches the given total investment.

Finding the Difference Between Investments

Finally, we need to calculate the difference between Ritik's and Sanjay's investments.

• Difference = Ritik's Investment - Sanjay's Investment
• Difference = $54,800 - 7,600$
• Difference = $\\text{₹}47,200$

Therefore, the difference between their investments was ₹47,200.