Profit Sharing Calculation: Difference Between Q and R

This problem involves calculating the difference in profit shares between partners Q and R, based on their investment ratio and the total profit earned.

1. Determine the Total Ratio Parts

The investment ratio of P, Q, and R is given as 59 : 14 : 72.

Total ratio parts = Sum of individual ratios

Total parts = $ 59 + 14 + 72 = 145 $

2. Calculate the Difference in Ratio Parts (Q and R)

We need the difference between the shares of Q and R.

Difference in ratio parts = R's ratio - Q's ratio

Difference parts = $ 72 - 14 = 58 $

3. Calculate the Value of One Ratio Part

The total profit earned is ₹4,790, distributed according to the total ratio parts (145).

Value of 1 ratio part = Total Profit / Total Ratio Parts

Value per part = $ \frac{4790}{145} $

To simplify, divide both numerator and denominator by 5:

Value per part = $ \frac{4790 \div 5}{145 \div 5} = \frac{958}{29} $

Since $ 58 = 2 \times 29 $, we can see a relationship.

4. Calculate the Difference in Profit Shares

The difference in shares is the difference in ratio parts multiplied by the value of one ratio part.

Difference in Shares = (Difference in ratio parts) $ \times $ (Value per part)

Difference in Shares = $ 58 \times \frac{958}{29} $

Since $ 58 = 2 \times 29 $, we can substitute:

Difference in Shares = $ (2 \times 29) \times \frac{958}{29} $

Cancel out the 29:

Difference in Shares = $ 2 \times 958 $

Difference in Shares = $ 1916 $

Therefore, the difference between the shares of Q and R is ₹1,916.