Understanding Profit Sharing Based on Investment Ratio

This problem involves calculating the profit share of individuals based on their investment ratio and determining the difference between two specific shares.

Investment Ratio and Total Profit

The investments made by P, Q, and R are in the ratio 34:75:6.

The total profit earned at the end of the year is ₹3,600.

Calculating the Sum of Ratio Parts

To determine each person's share of the profit, we first need to find the sum of the ratio parts:

Sum of ratio parts = $34 + 75 + 6 = 115$

Calculating Individual Profit Shares

Each person's share of the profit is calculated by multiplying their part of the ratio by the total profit, divided by the sum of the ratio parts.

• P's share = $\frac{34}{115} \times 3600$
• Q's share = $\frac{75}{115} \times 3600$
• R's share = $\frac{6}{115} \times 3600$

Finding the Difference Between Q's and R's Shares

The question asks for the difference between the shares of Q and R. We can calculate this directly:

Difference = Q's share - R's share

Difference = $\left( \frac{75}{115} \times 3600 \right) - \left( \frac{6}{115} \times 3600 \right)$

We can factor out the common terms:

Difference = $\left( \frac{75 - 6}{115} \right) \times 3600$

Difference = $\left( \frac{69}{115} \right) \times 3600$

Simplifying the Calculation

The fraction $\frac{69}{115}$ can be simplified. Both 69 and 115 are divisible by 23:

• $69 \div 23 = 3$
• $115 \div 23 = 5$

So, the fraction simplifies to $\frac{3}{5}$.

Now, calculate the difference:

Difference = $\frac{3}{5} \times 3600$

Difference = $3 \times \frac{3600}{5}$

Difference = $3 \times 720$

Difference = ₹2,160

Conclusion

The difference between the shares of Q and R is ₹2,160.