Comparing Quantities (NCERT Ch. 8)

• Convert between fractions, decimals, and percentages.
• Calculate percentage increase/decrease.
• Solve problems on profit, loss, simple interest, and discount.

1. Percentage means "per hundred" — to convert a fraction to a percentage, multiply by 100.
2. Profit = Selling Price (SP) − Cost Price (CP), when SP > CP. Loss = CP − SP, when CP > SP.
3. Profit % = (Profit/CP) x 100; Loss % = (Loss/CP) x 100.
4. Simple Interest (SI) = (Principal x Rate x Time) / 100.
5. Discount = Marked Price (MP) − Selling Price (SP); Discount % = (Discount/MP) x 100.

A shopkeeper buys a toy for ₹200 and sells it for ₹250. Find the profit percentage.

Profit = 250 - 200 = 50
Profit % = (50/200) x 100 = 25%

• Calculating profit/loss percentage on Selling Price instead of Cost Price (always use CP).
• Forgetting to divide the rate by 100 in the Simple Interest formula.
• Confusing Marked Price (before discount) with Selling Price (after discount).

• Convert 3/4 to a percentage.
• Find the SI on ₹1000 at 5% per annum for 2 years.

Open the Practice tab for graded questions on Comparing Quantities (NCERT Ch. 8).