The total expenditure of a family in 1920 is Rs. 8,000. The cost of living indext for the year 1920 taking 1910 as the base year is 160. Then the expenditure of the family in the year 1910 was `"_______".`

Options

A. Rs. 3000
B. Rs. 4000
C. Rs. 5000
D. Rs. 6000

Explanation

To find the expenditure of the family in the year 1910, we can use the formula for the cost of living index. The formula is given by:

\[ \text{Cost of Living Index} = \frac{\text{Total Expenditure in 1920}}{\text{Total Expenditure in 1910}} \times 100 \]

Given:
- Total Expenditure in 1920 = Rs. 8000
- Cost of Living Index for 1920 (taking 1910 as the base year) = 160

We can rearrange the formula to find the Total Expenditure in 1910:

\[ \text{Total Expenditure in 1910} = \frac{\text{Total Expenditure in 1920} \times 100}{\text{Cost of Living Index}} \]

Now, substituting the known values into the equation:

\[ \text{Total Expenditure in 1910} = \frac{8000 \times 100}{160} \]

Calculating the right side:

1. First, multiply 8000 by 100:
\[ 8000 \times 100 = 800000 \]

2. Now, divide 800000 by 160:
\[ \frac{800000}{160} = 5000 \]

Thus, the expenditure of the family in the year 1910 was Rs. 5000.

### Final Answer:
The expenditure of the family in the year 1910 was Rs. 5000.

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