Class 7 — Mathematics (NCERT)
Comparing Quantities
Class 7
- ✓By the end of this lesson students will be able to understand the meaning of percentage and convert fractions/decimals to percentages and vice-versa.
- ✓By the end of this lesson students will be able to calculate profit and loss, and profit/loss percentage.
- ✓By the end of this lesson students will be able to calculate simple interest, principal, time, and rate.
- ✓By the end of this lesson students will be able to apply these concepts to solve real-life problems involving money and quantities.
Key concepts
Percentage is a way of comparing quantities. The word 'per cent' means 'per hundred'. It is represented by the symbol '%'. For example, 15% means 15 out of 100. Percentages can be used to compare parts of a whole.
When articles are bought and sold, there can be a profit or a loss. The price at which an article is purchased is called the Cost Price (C.P.). The price at which an article is sold is called the Selling Price (S.P.).\n\nProfit: If the Selling Price (S.P.) is greater than the Cost Price (C.P.), there is a profit. (S.P. > C.P.)\nLoss: If the Selling Price (S.P.) is less than the Cost Price (C.P.), there is a loss. (S.P. < C.P.)
When we borrow money from a bank or a person, we usually have to pay some extra money for using their money. This extra money is called Interest. The money borrowed or lent is called the Principal (P). The rate at which the interest is calculated is called the Rate (R), usually given as a percentage per annum (p.a.). The period for which the money is borrowed or lent is called the Time (T), always in years. The total money to be paid back is called the Amount (A), which is the sum of the Principal and the Interest.
Key facts to remember
- 1Percentage means 'per hundred' and is denoted by '%'.
- 2Profit occurs when Selling Price (S.P.) is greater than Cost Price (C.P.).
- 3Loss occurs when Selling Price (S.P.) is less than Cost Price (C.P.).
- 4Profit % and Loss % are always calculated on the Cost Price (C.P.).
- 5Simple Interest (S.I.) is the extra money paid for using borrowed money.
- 6The formula for Simple Interest is S.I. = (P × R × T) / 100, where T must be in years.
- 7Amount (A) = Principal (P) + Simple Interest (S.I.).
Worked examples
Example 1
a) Express 4/5 as a percentage. b) Find 30% of ₹1500.
Answer
a) 80% b) ₹450
Example 2
A shopkeeper bought a bicycle for ₹1200 and sold it for ₹1380. Find the profit or loss and the profit or loss percentage.
Answer
Profit = ₹180, Profit Percentage = 15%
Remember that profit or loss percentage is always calculated on the Cost Price (C.P.).
Example 3
Find the simple interest on ₹4000 at 8% per annum for 2 years. Also, calculate the amount to be paid back.
Answer
Simple Interest = ₹640, Amount = ₹4640
Common mistakes
- ✗Calculating profit or loss percentage on the Selling Price (S.P.) instead of the Cost Price (C.P.).
- ✗Not converting the time period into years when calculating Simple Interest.
- ✗Confusing the formulas for profit and loss, or misidentifying whether a situation results in profit or loss.
- ✗Incorrectly converting percentages to fractions/decimals or vice-versa (e.g., multiplying by 100 instead of dividing when converting % to fraction).
- ✗Forgetting to add the Principal to the Simple Interest to find the total Amount.
Exam tips
- ★Read the question carefully to identify all given values (C.P., S.P., P, R, T) and what needs to be found.
- ★Always write down the correct formula before substituting the values. This helps in showing your understanding and can earn partial marks.
- ★Show all your working steps clearly and neatly. Avoid skipping steps, especially in multi-part problems.
- ★Double-check your calculations, especially for percentages and interest, to avoid arithmetic errors.
- ★Ensure that the units are consistent, particularly for time in Simple Interest problems (always convert to years).
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