Price of a commodity has in creased by 60%. By what per cent must a consumer reduce the consumption of the commodity so as not to increase the expenditure ?

Options

A. 37
B. 37.5
C. 50.5
D. 60

Answer

To solve the problem, we need to determine the percentage by which a consumer must reduce their consumption of a commodity to keep their expenditure unchanged after a 60% increase in the price of that commodity.

### Step-by-Step Solution:

1. **Understand the Initial Situation:**
Let's assume the initial price of the commodity is \( P \) and the initial quantity consumed is \( Q \). Therefore, the initial expenditure \( E \) can be calculated as:
\[ E = P \times Q \]

2. **Calculate the New Price:**
Since the price has increased by 60%, the new price \( P' \) can be calculated as:
\[ P' = P + 0.6P = 1.6P \]

3. **Set Up the Equation for Expenditure:**
To keep the expenditure the same after the price increase, the new expenditure \( E' \) must equal the initial expenditure \( E \). The new expenditure can be expressed as:
\[ E' = P' \times Q' = 1.6P \times Q' \]
where \( Q' \) is the new quantity consumed.

4. **Equate the Expenditures:**
Set the initial expenditure equal to the new expenditure:
\[ P \times Q = 1.6P \times Q' \]

5. **Simplify the Equation:**
We can divide both sides by \( P \) (assuming \( P \neq 0 \)):
\[ Q = 1.6 \times Q' \]

6. **Solve for the New Quantity:**
Rearranging the equation gives:
\[ Q' = \frac{Q}{1.6} \]

7. **Calculate the Reduction in Consumption:**
The reduction in consumption is given by:
\[ \text{Reduction} = Q - Q' = Q - \frac{Q}{1.6} = Q \left(1 - \frac{1}{1.6}\right) \]
Simplifying this further:
\[ \text{Reduction} = Q \left(\frac{1.6 - 1}{1.6}\right) = Q \left(\frac{0.6}{1.6}\right) = \frac{0.6Q}{1.6} = \frac{3Q}{8} \]

8. **Calculate the Percentage Reduction:**
The percentage reduction in consumption is:
\[ \text{Percentage Reduction} = \left(\frac{\text{Reduction}}{Q}\right) \times 100 = \left(\frac{\frac{3Q}{8}}{Q}\right) \times 100 = \frac{3}{8} \times 100 = 37.5\% \]

### Final Answer:
The consumer must reduce their consumption by **37.5%** to keep their expenditure unchanged.