The total expenditure of a family in \[1920\] is \[8000\]. The cost of living index for the year \[1920\] taking \[1910\] as the base year is \[160\]. Then, the expenditure of the family in the year \[1910\] was
a. \[3000\]
b. \[4000\]
c. \[5000\]
d. \[6000\]

Hint: From the question we have been given the total expenditure of the year \[1920\] and also we are given the cost of living index and are asked to find the expenditure of family in the year \[1910\]. For solving this question we will assume the expenditure of the family in the year \[1910\] as x and we will use the basic mathematical operation like division etc..and get the required solution.

Complete step by step solution:
Firstly, let us assume that the expenditure of the family in the year \[1910\] as x.
Given that the expenditure of a family in \[1920\]\[=8000\]
Cost of living \[=160\]
We know that,
Cost of living can be expressed using the basic mathematical operation which is division and multiplication as follows.
Cost of living\[=\dfrac{the\text{ expenditure of a family in 1920}}{the\text{ expenditure of a family in 1910}}\times 100\]
So, we will use the substitution method and will substitute the values in the above equation.
So, we get the equation reduced as follows.
\[\Rightarrow 160=\dfrac{8000}{x}\times 100\]
Now, we will make the x as subject and send remaining terms to one side of the equation. So, we get,
\[\Rightarrow x=\dfrac{8000}{160}\times 100\]
\[\Rightarrow x=50\times 100\]
\[\Rightarrow x=5000\]

So, the correct answer is “Option c”.

Note: Students must be very careful in doing the calculations. Students should be able to understand the question, they must know the basic operations. Students should not do mistake like if we write as \[ 8000=\dfrac{160}{x}\times 100\] instead of \[ 160=\dfrac{8000}{x}\times 100\] then our solution is wrong.