If the price of sugar rises from 6 per kg to 7.50 per kg, a person having no increase in his expenditure on sugar, will have to reduce his consumption of sugar by

Options

A. 0.15
B. 0.2
C. 0.25
D. 0.3

Answer

To solve the problem, we need to determine how much the person has to reduce his consumption of sugar due to the price increase while keeping his expenditure constant.

### Step-by-Step Solution:

1. **Identify the Initial and New Prices**:
- Initial price of sugar = ₹6 per kg
- New price of sugar = ₹7.50 per kg

2. **Calculate the Increase in Price**:
- Increase in price = New price - Initial price
- Increase in price = ₹7.50 - ₹6.00 = ₹1.50 per kg

3. **Let’s Assume the Person's Initial Expenditure**:
- Let the initial expenditure on sugar be 'E'.
- If the person buys 'x' kg of sugar at the initial price, then:
\[ E = 6x \]

4. **Determine the New Quantity of Sugar Purchased**:
- With the new price, the person can still spend the same amount 'E' but at the new price:
\[ E = 7.50y \]
- Where 'y' is the new quantity of sugar purchased.

5. **Set the Expenditures Equal**:
- Since the expenditure remains the same:
\[ 6x = 7.50y \]

6. **Express 'y' in Terms of 'x'**:
- Rearranging the equation gives:
\[ y = \frac{6x}{7.50} \]

7. **Calculate the Reduction in Consumption**:
- The reduction in consumption is:
\[ \text{Reduction} = x - y \]
- Substitute 'y':
\[ \text{Reduction} = x - \frac{6x}{7.50} \]
- Simplifying this:
\[ \text{Reduction} = x \left(1 - \frac{6}{7.50}\right) \]
- Calculate \( \frac{6}{7.50} \):
\[ \frac{6}{7.50} = 0.8 \]
- Therefore:
\[ \text{Reduction} = x(1 - 0.8) = 0.2x \]

8. **Conclusion**:
- The person will have to reduce his consumption of sugar by 0.2 kg for every kg he initially purchased.

### Final Answer:
The person will have to reduce his consumption of sugar by 0.2 kg.