Four people decided to start a restaurant by sharing an equal amount of the total investment. After some calculations they found that if they get two more equal investors, each of the four will have to pay Rs. 12000 less. What was the total investment?

Options

A. Rs 24000
B. Rs 72000
C. rs 144000
D. Rs 288000

Answer

To solve the problem, let's denote the total investment as \( T \).

1. **Initial Investment per Person**:
When there are 4 people, the investment per person is given by:
\[ \text{Investment per person} = \frac{T}{4} \]

2. **Investment per Person with 2 More Investors**:
If 2 more investors join, there will be a total of 6 investors. The new investment per person will be:
\[ \text{New investment per person} = \frac{T}{6} \]

3. **Difference in Investment**:
According to the problem, the difference in the amount each person has to pay when 2 more investors join is Rs. 12000. Therefore, we can set up the equation:
\[ \frac{T}{4} - \frac{T}{6} = 12000 \]

4. **Finding a Common Denominator**:
To solve the equation, we need a common denominator for the fractions. The least common multiple of 4 and 6 is 12. We can rewrite the equation:
\[ \frac{3T}{12} - \frac{2T}{12} = 12000 \]

5. **Simplifying the Equation**:
Now, simplify the left side:
\[ \frac{3T - 2T}{12} = 12000 \]
This simplifies to:
\[ \frac{T}{12} = 12000 \]

6. **Solving for Total Investment**:
To find \( T \), multiply both sides by 12:
\[ T = 12000 \times 12 \]
\[ T = 144000 \]

Thus, the total investment is Rs. 144000.