# Comparing Quantities Class 7 Notes: Chapter 8

Quite often, in our daily life, we are required to compare two quantities. Let us look at a few points on how a comparison between two or more objects can be done.

• It is to be noted that the comparison between any two quantities can be written as a ratio.
• To compare two quantities, their units must be the same.
• Different ratios can also be compared with each other to know if they are equivalent or not.
• Two ratios can be compared by converting them to like fractions. If the two fractions are equal, we say the two given ratios are equivalent. If two ratios are equivalent, then the four quantities are said to be in proportion. For example, 4:16 and 8:32 are equivalent, therefore, the numbers 4,16,8 and 32 are said to be in proportion.
• Another way of comparing quantities is by percentage. Percentages have numerators of fractions with a denominator of 100.
• Fractions can be converted to percentages and vice-versa. For example, $\frac{2}{5}\times 100=40\%$, likewise, $25\%=\frac{25}{100}=\frac{1}{4}$

## Comparing Quantities Class 7 Formulas

 Term Formula Discounts It is the reduction given to the marked price (MP) of an article. One can find the discount by subtracting the discounted price from its marked price. Discount = Marked Price – Sales Price Profit and Loss Profit is the money made from selling the item for a price greater than the cost price. It can be calculated as follows: Profit = S.P – C.P Loss is the money lost by selling an item for a lesser price than the cost price. It can be calculated as Loss = C.P – S.P Sales Tax and VAT Sales tax is the amount charged by the government on the sale of an item. Value added tax (VAT) is again the amount charged by the government on the sale of an item. This is collected by the shopkeeper from the customer and later given to the government. If the tax is x%, then the final price of an item including the tax would be $Final \:Price = Cost \:of \:an \:item + (\frac{x}{cost \:of \:an \:item}) \times 100$ Interest The extra money paid to institutions such as banks and post offices on money deposited with them Simple Interest Simple interest is calculated using the formula: $SI=\frac{P\times R\times T}{100}$ Where, P is the principal R is the rate of interest T is the time Compound Interest Compound Interest is calculated using the formula $A=P(1+\frac{R}{100})^{n}$ Where, P is the principal R is the rate of interest n is the time for which the money is deposited or borrowed

### Comparing Quantities Class 7 questions

1. Convert each part of the ratio to percentage:
1. 1:3
2. 4:6:8
3. 1:2: 5
1. The population of a city decreased from 55,000 to 25,500. Find the percentage decrease.
2. Juhi sells a refrigerator for 15,500. She loses 20% in the bargain. What was the price at which she bought it?
3. Find the amount to be paid at the end of 3 years in each case:
1. Principal = 2,200 at 14% p.a.
2. Principal = 10,500 at 5% p.a.
1. If Meena gives an interest of 45 for one year at 9% rate p.a. What is the sum she has borrowed?

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