12) A, B, and C invest 63000, 56000, and 84000 respectively to start a business. After one year, the profit is distributed in the ratio of their investments. If C's share of profit is Rs.54000, find the total profit earned.

To find the total profit earned, we start by determining the ratio of investments made by A, B, and C.

The investments are:
- A's investment = 63,000
- B's investment = 56,000
- C's investment = 84,000

The ratio of their investments is:

\[
\text{Ratio} = 63,000 : 56,000 : 84,000
\]

We simplify this ratio by dividing each term by their greatest common divisor (GCD). The GCD of 63,000, 56,000, and 84,000 is 7,000.

\[
\text{Ratio} = \frac{63,000}{7,000} : \frac{56,000}{7,000} : \frac{84,000}{7,000}
\]
\[
\text{Ratio} = 9 : 8 : 12
\]

So, the profit distribution ratio is \( 9 : 8 : 12 \).

Let's denote the total profit by \( P \). Then, C's share of the profit is given by:

\[
C's\ share = \frac{12}{9+8+12} \times P = \frac{12}{29} \times P
\]

We know that C's share is Rs. 54,000, so:

\[
\frac{12}{29} \times P = 54,000
\]

To find the total profit \( P \), we solve for \( P \):

\[
P = \frac{54,000 \times 29}{12}
\]

Calculating this:

\[
P = \frac{1,566,000}{12} = 130,500
\]

So, the total profit earned is **Rs. 1,30,500**.

Would you like more details or have any questions?

Here are five related questions for further practice:
1. If the profit ratio was instead 10:7:13, what would be C's share if the total profit was Rs. 200,000?
2. What would be A's share if the total profit was Rs. 100,000 with the given investment ratio?
3. If B's share of the profit was Rs. 48,000, what would be the total profit?
4. How would the total profit change if C's investment increased by 10% while A and B's investments remained the same?
5. If A withdrew Rs. 10,000 from his investment, how would the profit distribution change?

**Tip:** When dealing with ratios, always simplify the numbers to their smallest form to make calculations easier.

A, B, and C invest 63000, 56000, and 84000 respectively to start a business. After one year, the profit is distributed in the ratio of their investments. If C's share of profit is Rs.54000, find the total profit earned.

Learn how to calculate the total profit earned in a business based on the investments made by A, B, and C, with a detailed step-by-step solution. Understand the concept of profit distribution in ratio and proportion. This problem is suitable for students in Grades 6-8.

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