NCERT Solutions Class 8 Maths Chapter 8 — Comparing Quantities

Solution:

Step 1: Let the original price be ₹100.

Step 2: Increasing by 20%: New price = 100 + (20/100) × 100 = 100 + 20 = ₹120.

Step 3: Decreasing the new price by 20%: Decrease amount = (20/100) × 120 = ₹24.

Step 4: Final price = 120 - 24 = ₹96. Since ₹96 < ₹100, the final price is less than the original price.

Solution:

Step 1: Profit is defined as the excess amount received from selling an item over its cost.

Step 2: Mathematically, Profit = Selling Price (SP) - Cost Price (CP).

Step 3: For profit to be positive (i.e., a profit is made), SP must be greater than CP.

Solution:

Step 1: Let the total number of students be 'X'.

Step 2: According to the problem, 40% of X is 240.

Step 3: This can be written as (40/100) × X = 240.

Step 4: Solving for X: X = (240 × 100) / 40 = 6 × 100 = 600.

Solution:

Step 1: Rahul's profit amount is ₹240 - ₹200 = ₹40, which is correct.

Step 2: Profit percentage is calculated as (Profit / Cost Price) × 100%.

Step 3: Rahul used the Selling Price (₹240) in the denominator instead of the Cost Price (₹200).

Step 4: The correct calculation should be (₹40 / ₹200) × 100% = 20%.

Solution:

Step 1: The Marked Price (MP) is the price listed on the item.

Step 2: The Discount (D) is the reduction offered on the MP.

Step 3: The Selling Price (SP) is the price the customer actually pays after the discount.

Step 4: Therefore, Selling Price = Marked Price - Discount, or SP = MP - D.

Step 5: Rearranging this, we get Discount = Marked Price - Selling Price, or D = MP - SP.