The price of sugar increases from ₹20/kg to ₹30/kg. By what percent consumption must be decreased to maintain the same expenditure

Questions : The price of sugar increases from ₹20/kg to ₹30/kg. By what percent consumption must be decreased to maintain the same expenditure?

Answer:  

 We can use the same shortcut formula for percentage decrease:

$$\text{Required Percentage Decrease} = \frac{\text{Increase Percentage}}{100 + \text{Increase Percentage}} \times 100$$

Step 1: Calculate the Percentage Increase in Price

The price increases from ₹20/kg to ₹30/kg, so the percentage increase is:

$$\frac{30 - 20}{20} \times 100 = \frac{10}{20} \times 100 = 50\%$$

Step 2: Apply the Shortcut Formula

$$\text{Required Percentage Decrease} = \frac{50}{100 + 50} \times 100$$ $$= \frac{50}{150} \times 100$$ $$= \frac{1}{3} \times 100$$ $$= 33.33\%$$

Final Answer

The consumption must be decreased by 33.33% to maintain the same expenditure.

Additional Methods 

Here's how to calculate the percentage decrease in consumption needed to maintain the same expenditure:

1. Understand the relationship:

• Expenditure = Price * Consumption

2. Set up the equation:

Let:

• P1 = Original price (₹20/kg)
• C1 = Original consumption (unknown)
• P2 = New price (₹30/kg)
• C2 = New consumption (unknown)

Since the expenditure remains the same:

P1 * C1 = P2 * C2

3. Solve for the ratio of consumptions:

20 * C1 = 30 * C2

C1 / C2 = 30 / 20

C1 / C2 = 3 / 2

This means the original consumption (C1) was 3/2 times the new consumption (C2).

4. Calculate the percentage decrease:

• Decrease in consumption = C1 - C2
• Percentage decrease = (Decrease in consumption / Original consumption) * 100
• Percentage decrease = ((C1 - C2) / C1) * 100

Substitute C1 = (3/2) * C2:

Percentage decrease = (((3/2) * C2 - C2) / ((3/2) * C2)) * 100

Percentage decrease = ((1/2) * C2 / (3/2) * C2) * 100

Percentage decrease = (1/3) * 100

Percentage decrease = 33.33% (approximately)

Answer: The consumption must be decreased by approximately 33.33% to maintain the same expenditure.

Short Cut 

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