A person increases his consumption of sugar by 42.84% because the price of sugar is reduced by x%. Find x? (expenditure remains Constant)

Options

A. 32
B. 35
C. 30
D. 28

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript and break it down into clear steps.

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the percentage decrease in the price of sugar (denoted as x%) given that the consumption of sugar has increased by 42.84% while the expenditure remains constant.

2. **Assume Initial Values**:
- Let the initial price of sugar be ₹100.
- Let the initial quantity of sugar consumed be Q (we will calculate this later).
- Let the total expenditure be ₹10,000 (which remains constant).

3. **Calculate Initial Quantity**:
- Since expenditure = Price × Quantity, we have:
\[ 10,000 = 100 \times Q \]
- Solving for Q gives:
\[ Q = \frac{10,000}{100} = 100 \text{ kg} \]

4. **Calculate New Quantity After Increase**:
- The consumption of sugar is increased by 42.84%. Therefore, the new quantity (Q') is:
\[ Q' = Q + (42.84\% \text{ of } Q) = 100 + (0.4284 \times 100) = 100 + 42.84 = 142.84 \text{ kg} \]

5. **Calculate New Price**:
- Since the expenditure remains constant at ₹10,000, we can find the new price (P') using the formula:
\[ \text{Expenditure} = \text{New Price} \times \text{New Quantity} \]
- Thus,
\[ 10,000 = P' \times 142.84 \]
- Solving for P' gives:
\[ P' = \frac{10,000}{142.84} \approx 70 \text{ (rounded)} \]

6. **Calculate Change in Price**:
- The original price was ₹100, and the new price is approximately ₹70. The change in price is:
\[ \text{Change in Price} = 100 - 70 = 30 \]

7. **Calculate Percentage Decrease in Price (x%)**:
- The percentage decrease in price is calculated as:
\[ x = \left(\frac{\text{Change in Price}}{\text{Original Price}}\right) \times 100 = \left(\frac{30}{100}\right) \times 100 = 30\% \]

### Conclusion:
The percentage decrease in the price of sugar (x) is **30%**.

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