Quantitative Aptitude Problem 3 Continued Proportion

 

How to Solve Continued Proportion Problems Easily

Question:

Numbers A, B, C, and D are in continued proportion. If A = 20 and C = 180, find the sum of B and D.

Step-by-Step Solution:

Step 1: Understanding Continued Proportion

In continued proportion, the relationship between numbers follows the rule:

$$A : B = B : C = C : D$$

This means:

$$B^2 = A \times C$$ $$D = \frac{C^2}{B}$$

Step 2: Finding B

$$B^2 = 20 \times 180$$ $$B^2 = 3600$$ $$B = \sqrt{3600} = 60$$

Step 3: Finding D

$$D = \frac{C^2}{B} = \frac{180^2}{60}$$ $$D = \frac{32400}{60} = 540$$

Step 4: Finding the Sum of B and D

$$B + D = 60 + 540 = 600$$

Final Answer:

The sum of B and D is 600.

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How to find numbers in proportion
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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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Quantitative Aptitude Problem 1 Profit or Loss Percentage

How to Calculate Profit or Loss Percentage? Step-by-Step Solution with Formula

Question:

The profit obtained by selling a product for ₹2500 is the same as the loss incurred when selling it for ₹1900. If the product is sold for ₹2400, what is the profit or loss percentage?

Step-by-Step Solution:

Step 1: Understanding the Given Condition

Let the cost price (CP) of the product be ₹x.

• Profit at ₹2500 = Loss at ₹1900
• This means: $$2500 - x = x - 1900$$

Step 2: Finding the Cost Price

Solving for x:

$$2x = 4400$$ $$x = 2200$$

So, the cost price of the product is ₹2200.

Step 3: Finding Profit or Loss at ₹2400

• Selling Price (SP) = ₹2400
• Since SP > CP, there is a profit: $$\text{Profit} = 2400 - 2200 = 200$$

Step 4: Calculating Profit Percentage

$$\left( \frac{200}{2200} \right) \times 100 = 9.09\%$$

Final Answer:

Profit of 9.09 percent when selling at ₹2400.

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How to calculate profit percentage
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