P and Q started a business by investing Rs 156000 and Rs 117000 respectively and their time period of investment is same. If P's share in the profit earned by them is Rs 12000, then what is the total profit earned by both of them together?

Options

A. 25000
B. 17000
C. 21000
D. 18000

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript and break it down into clear steps.

### Step 1: Identify the investments of P and Q
- P invested Rs 156,000.
- Q invested Rs 117,000.

### Step 2: Set up the profit-sharing ratio
Since the time period of investment is the same for both P and Q, the profit-sharing ratio can be determined by their investments.

The profit share is proportional to the investment:
- Profit share of P : Profit share of Q = Investment of P : Investment of Q

Thus, we can write:
\[ \text{Profit share of P} : \text{Profit share of Q} = 156000 : 117000 \]

### Step 3: Simplify the ratio
To simplify the ratio, we can divide both sides by 39,000:
\[ \frac{156000}{39000} : \frac{117000}{39000} = 4 : 3 \]

So, the profit-sharing ratio of P to Q is 4:3.

### Step 4: Calculate the total parts in the profit-sharing ratio
The total parts in the profit-sharing ratio can be calculated as:
\[ 4 + 3 = 7 \text{ parts} \]

### Step 5: Determine P's share in terms of total profit
We know from the problem that P's share in the profit is Rs 12,000. Since P's share corresponds to 4 parts of the total profit, we can set up the equation:
\[ \text{P's share} = \frac{4}{7} \times \text{Total Profit} \]
Let the total profit be denoted as \( T \):
\[ 12000 = \frac{4}{7} T \]

### Step 6: Solve for the total profit \( T \)
To find \( T \), we can rearrange the equation:
\[ T = 12000 \times \frac{7}{4} \]
Calculating this gives:
\[ T = 12000 \times 1.75 = 21000 \]

### Conclusion
The total profit earned by both P and Q together is Rs 21,000.

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