Avinash , Manoj and Arun started a business in partnership investing in the ratio `3:2:5` respecitvley. At the end of the year, they earned a profit of X 45000 which is 15% of their total investment. How much did Manoj invest ?

Options

A. X 60000
B. X 180000
C. X 30000
D. X 90000

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the Profit and Investment Relationship
We know that the profit earned at the end of the year is ₹45,000, which is 15% of the total investment.

### Step 2: Calculate the Total Investment
To find the total investment, we can use the formula for percentage:

\[ \text{Total Investment} = \frac{\text{Profit}}{\text{Percentage}} \times 100 \]

Substituting the values we have:

\[ \text{Total Investment} = \frac{45000}{15} \times 100 \]

Calculating this gives:

\[ \text{Total Investment} = 3000 \times 100 = 300000 \]

So, the total investment is ₹3,00,000.

### Step 3: Determine the Ratio of Investments
The investment ratio among Avinash, Manoj, and Arun is given as 3:2:5.

### Step 4: Calculate the Total Parts in the Ratio
To find out how much each person invested, we first need to calculate the total parts in the ratio:

\[ \text{Total parts} = 3 + 2 + 5 = 10 \]

### Step 5: Calculate Manoj's Investment
Manoj's share in the investment is represented by the part corresponding to him in the ratio, which is 2.

To find Manoj's investment, we use the formula:

\[ \text{Manoj's Investment} = \left(\frac{\text{Manoj's Ratio}}{\text{Total Parts}}\right) \times \text{Total Investment} \]

Substituting the values:

\[ \text{Manoj's Investment} = \left(\frac{2}{10}\right) \times 300000 \]

Calculating this gives:

\[ \text{Manoj's Investment} = \frac{600000}{10} = 60000 \]

Thus, Manoj invested ₹60,000.

### Final Answer
Manoj invested ₹60,000.

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