Understanding Profit Distribution in Ratios

This problem involves calculating the distribution of a total profit based on the investment ratios of partners. The profit earned by each partner is directly proportional to their investment.

Calculating Total Ratio Parts

The investment ratio for partners A, B, and C is given as 61 : 43 : 90.

To find the total value represented by these ratios, we sum them up:

Total Ratio Parts = $61 + 43 + 90 = 194$

Determining the Value of One Ratio Part

The total profit earned at the end of the year is ₹2,910.

This total profit corresponds to the sum of the ratio parts (194).

We can find the profit amount represented by one part of the ratio by dividing the total profit by the total ratio parts:

Value of 1 Ratio Part = Total Profit / Total Ratio Parts

Value of 1 Ratio Part = $₹2,910 / 194$

Value of 1 Ratio Part = $₹15$

Calculating Individual Profit Shares (Optional but helpful for clarity)

Now we can find the profit share for each partner:

• A's Share = $61 * ₹15 = ₹915$
• B's Share = $43 * ₹15 = ₹645$
• C's Share = $90 * ₹15 = ₹1350$

Checking the total: $₹915 + ₹645 + ₹1350 = ₹2910$, which matches the total profit.

Finding the Difference Between B's and C's Share

The question asks for the difference between the share of B and C.

Difference = C's Share - B's Share

Difference = $₹1350 - ₹645$

Difference = $₹705$

Alternative Method: Difference in Ratio Parts

We can also calculate the difference directly using the ratio parts:

Difference in Ratio Parts (C - B) = $90 - 43 = 47$

Difference in Profit = Difference in Ratio Parts * Value of 1 Ratio Part

Difference in Profit = $47 * ₹15$

Difference in Profit = $₹705$

Both methods confirm that the difference between the share of B and C is ₹705.