Quantitative Aptitude Problem 2 How to Calculate Percentage Decrease in Consumption When Price Increases

How to Calculate Percentage Decrease in Consumption When Price Increases

Question:

The price of petrol increased by 20%, due to which Rahul decreased his consumption by x%. Even after reducing consumption, his total expense increased by 4%. Find the value of x.

Step-by-Step Solution:

Step 1: Understanding the Relationship

Total expense on petrol is given by:

$$\text{Expense} = \text{Price per liter} \times \text{Quantity consumed}$$

Let the initial price of petrol be ₹P and initial consumption be Q liters.

Thus, the initial expense = P × Q.

Now, the price increases by 20%, making the new price:

$$\text{New price} = 1.2P$$

Rahul reduces his consumption by x%, meaning his new consumption is:

$$\text{New quantity} = Q \times \left(1 - \frac{x}{100} \right)$$

Since his total expense increased by 4%, the new expense is:

$$1.04 \times P \times Q$$

Step 2: Setting Up the Equation

$$1.2P \times Q \times \left(1 - \frac{x}{100} \right) = 1.04PQ$$

Cancel P × Q on both sides:

$$1.2 \times \left(1 - \frac{x}{100} \right) = 1.04$$

Expanding the equation:

$$1.2 - \frac{1.2x}{100} = 1.04$$ $$1.2 - 1.04 = \frac{1.2x}{100}$$ $$0.16 = \frac{1.2x}{100}$$ $$x = \frac{0.16 \times 100}{1.2}$$ $$x = 13.33$$

Final Answer:

Rahul decreased his petrol consumption by 13.33%.

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