Expenses (in multiples of ₹10,000/-) on consumption of fuel for the official car at a regional office (RO) of a national organization during 2006-2010 is given below in a tabular form along with the National Average (NA) during the said period. It is given that there are five ROs.
`{:("Year",2006,2007,2008,2009,2010),("RO",20,22,23,24,25),("NA",18,17,19,18,23):}`
If the RO, given in the table, is not taken into account, then what would be the NA (in multiple of ₹10,000/-) in 2006?

Options

A. 17
B. 16.5
C. 17.5
D. 18

Answer

To find the National Average (NA) for the year 2006 when the expenses of the Regional Office (RO) are not taken into account, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the National Average for 2006**:
The National Average (NA) for 2006 is given as 18 (in multiples of ₹10,000).

2. **Calculate the Total Expenses for All ROs**:
Since there are 5 Regional Offices (ROs), the total expenses for all ROs in 2006 can be calculated as:
\[ \text{Total Expenses} = \text{NA} \times \text{Number of ROs} = 18 \times 5 = 90 \text{ (in multiples of ₹10,000)} \]

3. **Subtract the RO Expenses**:
The expenses for the specific RO in 2006 is given as 20 (in multiples of ₹10,000). Therefore, we subtract this from the total expenses:
\[ \text{Remaining Expenses} = \text{Total Expenses} - \text{RO Expenses} = 90 - 20 = 70 \text{ (in multiples of ₹10,000)} \]

4. **Calculate the New National Average**:
Now, we need to find the new National Average considering only the remaining 4 ROs. We calculate this by dividing the remaining expenses by the number of remaining ROs:
\[ \text{New NA} = \frac{\text{Remaining Expenses}}{\text{Number of Remaining ROs}} = \frac{70}{4} = 17.5 \text{ (in multiples of ₹10,000)} \]

### Final Answer:
The National Average (NA) in 2006, when the RO is not taken into account, is ₹17,500.

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