The average revenues of 7 consecutive years of a company is Rs. 75 lakhs. If the average of first 4 years is Rs. 70 lakhs and that of last 4 years is Rs. 82 lakhs, what will be the revenue for the 4th year ?

Options

A. Rs. 85 lakhs
B. Rs. 83 lakhs
C. Rs. 81 lakhs
D. Rs. 79 lakhs

Answer

To find the revenue for the 4th year based on the given information, we will follow these steps:

### Step 1: Calculate the total revenue for 7 years
The average revenue for 7 years is given as Rs. 75 lakhs. To find the total revenue for these 7 years, we multiply the average by the number of years.

\[ \text{Total Revenue} = \text{Average} \times \text{Number of Years} = 75 \text{ lakhs} \times 7 = 525 \text{ lakhs} \]

### Step 2: Calculate the total revenue for the first 4 years
The average revenue for the first 4 years is given as Rs. 70 lakhs. We calculate the total revenue for these 4 years similarly.

\[ \text{Total Revenue for First 4 Years} = 70 \text{ lakhs} \times 4 = 280 \text{ lakhs} \]

### Step 3: Calculate the total revenue for the last 4 years
The average revenue for the last 4 years is given as Rs. 82 lakhs. We calculate the total revenue for these 4 years.

\[ \text{Total Revenue for Last 4 Years} = 82 \text{ lakhs} \times 4 = 328 \text{ lakhs} \]

### Step 4: Set up the equation to find the revenue for the 4th year
The total revenue for the first 4 years includes the revenue for the 4th year, while the total revenue for the last 4 years also includes the revenue for the 4th year. To find the revenue for the 4th year, we can use the total revenues calculated:

Let \( R_4 \) be the revenue for the 4th year. The total revenue for the first 4 years can be expressed as:

\[ R_1 + R_2 + R_3 + R_4 = 280 \text{ lakhs} \quad (1) \]

The total revenue for the last 4 years can be expressed as:

\[ R_4 + R_5 + R_6 + R_7 = 328 \text{ lakhs} \quad (2) \]

### Step 5: Combine the equations
From equation (1), we can express \( R_1 + R_2 + R_3 \) as:

\[ R_1 + R_2 + R_3 = 280 - R_4 \]

From equation (2), we can express \( R_5 + R_6 + R_7 \) as:

\[ R_5 + R_6 + R_7 = 328 - R_4 \]

### Step 6: Calculate the total revenue excluding the 4th year
The total revenue for all 7 years can also be expressed as:

\[ (R_1 + R_2 + R_3) + (R_4) + (R_5 + R_6 + R_7) = 525 \text{ lakhs} \]

Substituting the expressions from above:

\[ (280 - R_4) + R_4 + (328 - R_4) = 525 \]

### Step 7: Simplify the equation
Combining the terms gives:

\[ 280 + 328 - R_4 = 525 \]

### Step 8: Solve for \( R_4 \)
Now, we can solve for \( R_4 \):

\[ 608 - R_4 = 525 \]
\[ R_4 = 608 - 525 = 83 \text{ lakhs} \]

### Conclusion
The revenue for the 4th year is Rs. 83 lakhs.

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