Profit Ratio Calculation: P, Q, R Investments

The problem requires calculating the difference in profit between partners based on their initial investments. Profit sharing in a business partnership is determined by the ratio of investments made by each partner.

Determine Investment Ratio

First, identify the ratio of investments made by P, Q, and R.

• P's Investment: ₹2,030
• Q's Investment: ₹1,700
• R's Investment: ₹1,010

The ratio of their investments is P : Q : R = 2030 : 1700 : 1010.

Simplify this ratio by dividing each amount by 10:

Simplified Investment Ratio = 203 : 170 : 101

Calculate Profit Difference

Q's share of the profit is given as ₹975. This amount corresponds to the 170 parts in the simplified investment ratio.

Determine the value of one part of the profit share:

Value of 170 parts (Q's Profit) = ₹975

Value of 1 part = $ \frac{975}{170} $

The question asks for the difference in profit earned by P and R. First, calculate the difference in their ratio parts:

Difference in Ratio Parts (P - R) = 203 (P's parts) - 101 (R's parts) = 102 parts

Now, calculate the profit difference corresponding to these 102 parts:

Profit Difference (P - R) = Value of 102 parts

Profit Difference (P - R) = $ 102 \times \frac{975}{170} $

Perform the calculation:

Profit Difference (P - R) = $ \frac{102}{170} \times 975 $

Simplify the fraction $ \frac{102}{170} $. Both numbers are divisible by 34 ($102 = 3 \times 34$ and $170 = 5 \times 34$).

Profit Difference (P - R) = $ \frac{3 \times 34}{5 \times 34} \times 975 = \frac{3}{5} \times 975 $

Calculate the final value:

Profit Difference (P - R) = $ 3 \times \frac{975}{5} = 3 \times 195 $

Profit Difference (P - R) = ₹585

Conclusion

The difference in profit earned by P and R is ₹585.