Quantitative Aptitude

Concept:
In profit and discount problems, three important prices are involved:

• Cost Price (CP) – The price at which the shopkeeper purchases the item.
• Marked Price (MP) – The price printed or listed on the product.
• Selling Price (SP) – The price at which the product is actually sold after giving discount.

The relationships used in such problems are:
Step 1: Find the Selling Price after discount.
Marked Price: Discount given: Selling Price:
Step 2: Use the profit formula.
The shopkeeper gains: Thus,
Step 3: Substitute the selling price.

Step 4: Final answer.

Concept:
In ratio problems involving ages, the given ratio represents the proportional relationship between the ages of two individuals. If the ratio of their ages is known, we can assume the ages to be multiples of the ratio values and then use the given sum to determine their actual ages. If the ratio of two quantities is: then their actual values can be represented as: where is a common multiplier.
Step 1: Represent the ages using the ratio.
The ratio of the ages of A and B is: Let their ages be:
Step 2: Use the given sum of ages.

Step 3: Find their present ages.

Step 4: Find their ages after 4 years.

Step 5: Find the new ratio.
Divide both numbers by 4:
Step 6: Final answer.

Concept:
When a train passes a pole or a standing object, the distance covered by the train is equal to the length of the train. The speed of the train can be calculated using the basic formula: Here:

• Distance = Length of the train
• Time = Time taken to completely pass the pole

After calculating speed in metres per second (m/s), we convert it into kilometres per hour (km/hr) using:
Step 1: Identify the given values.

Step 2: Calculate speed in m/s.

Step 3: Convert m/s to km/hr.

Step 4: Final result.

Concept:
When the price of a commodity increases but the total expenditure must remain constant, the quantity consumed must decrease proportionally. This relationship can be calculated using the formula: This formula helps determine how much consumption must be reduced so that the total spending does not change despite the price increase.
Step 1: Identify the given information.

Step 2: Apply the formula.

Step 3: Alternative explanation using numbers.
Assume initially: After a 25% increase: To keep the expenditure ₹100: Reduction in consumption:
Step 4: Selecting the correct answer.