The average revenues of 7 consecutive years of a company is Rs. 79 lakhs. If the average of first 4 years is Rs. 74 lakhs and that of last 4 years is Rs. 86 lakhs, what is the revenue for the 4th year?

Options

A. Rs. 87 lakhs
B. Rs. 89 lakhs
C. Rs. 85 lakhs
D. Rs. 83 lakhs

Answer

To find the revenue for the 4th year, we can follow these steps:

### Step 1: Calculate the total revenue for 7 years
Given that the average revenue for 7 consecutive years is Rs. 79 lakhs, we can calculate the total revenue for these 7 years.

\[ \text{Total Revenue for 7 years} = \text{Average} \times \text{Number of Years} = 79 \text{ lakhs} \times 7 = 553 \text{ lakhs} \]

### Step 2: Calculate the total revenue for the first 4 years
The average revenue for the first 4 years is given as Rs. 74 lakhs. We can calculate the total revenue for these 4 years.

\[ \text{Total Revenue for first 4 years} = 74 \text{ lakhs} \times 4 = 296 \text{ lakhs} \]

### Step 3: Calculate the total revenue for the last 4 years
The average revenue for the last 4 years is given as Rs. 86 lakhs. We can calculate the total revenue for these 4 years.

\[ \text{Total Revenue for last 4 years} = 86 \text{ lakhs} \times 4 = 344 \text{ lakhs} \]

### Step 4: Set up the equation for the 4th year
Let the revenue for the 4th year be denoted as \( R_4 \). The total revenue for the last 4 years includes the revenue for the 4th year, which is also part of the total revenue for the first 4 years. Therefore, we can express the total revenue for the 7 years as:

\[ \text{Total Revenue for 7 years} = \text{Total Revenue for first 4 years} + \text{Total Revenue for last 4 years} - R_4 \]

Substituting the values we calculated:

\[ 553 = 296 + 344 - R_4 \]

### Step 5: Solve for \( R_4 \)
Now, we can rearrange the equation to solve for \( R_4 \):

\[ 553 = 640 - R_4 \]

\[ R_4 = 640 - 553 = 87 \text{ lakhs} \]

### Conclusion
The revenue for the 4th year is Rs. 87 lakhs.

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