CBSE Class 7 Mathematics Percentage Notes Set 02

Ratio and Proportion

A ratio compares two quantities of the same kind in the same unit; a : b is the fraction a/b. Multiplying or dividing both terms by the same non-zero number gives an equivalent ratio, and a ratio is in simplest form when the HCF of its terms is 1. To compare ratios, write them as fractions with a common denominator.
Four numbers a, b, c, d are in proportion when a : b = c : d. Then the product of the extremes (a and d) equals the product of the means (b and c). If one term is missing, use this equality to find it. In the unitary method find the value of one unit first and then multiply.

Percentage

A percentage is a fraction with denominator 100. To change a fraction or decimal to a percentage multiply by 100; to change a percentage to a fraction or decimal divide by 100. To express one quantity as a percentage of another, bring both to the same unit and compute (part ÷ whole) × 100.
Percentage increase or decrease = (change ÷ original value) × 100, always on the original value. To find x% of a number, multiply the number by x/100. The remaining part of a whole is (100 - x)%.

Profit and Loss

The cost price (C.P.) is what is paid to buy or make an article, and any overheads such as repairs or transport are added to it. The selling price (S.P.) is what it is sold for. Profit = S.P. - C.P. when S.P. is greater, and Loss = C.P. - S.P. when C.P. is greater.
Profit percent = (profit ÷ C.P.) × 100 and loss percent = (loss ÷ C.P.) × 100; both are always taken on the cost price. S.P. = C.P. × (100 + profit%) ÷ 100 for a profit, and S.P. = C.P. × (100 - loss%) ÷ 100 for a loss. To find C.P. from S.P., use C.P. = S.P. × 100 ÷ (100 + profit%) or S.P. × 100 ÷ (100 - loss%).

Simple Interest

Interest is the extra money paid for using borrowed money. The sum borrowed is the principal (P), the yearly charge is the rate (R% per annum) and the duration is the time (T). Amount = principal + interest.
Simple interest S.I. = P × R × T ÷ 100, with T in years (3 months is 1/4 year, 20 months is 5/3 years). Rearranging, P = S.I. × 100 ÷ (R × T), R = S.I. × 100 ÷ (P × T) and T = S.I. × 100 ÷ (P × R).

Worked Example

Find the selling price of an article bought for Rs. 800 and sold at a loss of 15%.
Loss = 15% of 800 = Rs. 120, so S.P. = 800 - 120 = Rs. 680.