P , Q, and R invested ₹30,000, ₹40,000, and ₹50,000 respectively in a business. If the profit at the end of the year is ₹36,000, what is Q's share of the profit?

The correct option is ₹12,000.

Step 1: Understand the ratio of investments
When business partners invest capital for the same duration of time (1 year in this case), the total profit is divided among them in direct proportion to their initial investments.

The investments made by P, Q, and R are:
P's Investment = ₹30,000
Q's Investment = ₹40,000
R's Investment = ₹50,000

Step 2: Calculate the ratio of profit sharing
The ratio of their investments is:

$\text{Ratio of P : Q : R}=30000:40000:50000$

Simplifying the ratio by dividing each term by 10,000 gives:

$\text{Ratio of P : Q : R}=3:4:5$

Step 3: Calculate total ratio parts
Sum of the ratio parts:

$\text{Total parts}=3+4+5=12$

Step 4: Find Q's share of the profit
The total profit at the end of the year is ₹36,000.
Q's share corresponds to 4 parts out of the total 12 parts.

$\text{Q's Share}=\left(\frac{4}{12}\right)\times 36000$

$\text{Q's Share}=\left(\frac{1}{3}\right)\times 36000$

$\text{Q's Share}=12000$

Therefore, Q's share of the profit is ₹12,000.