# NCERT Class 8 Mathematics Chapter 8 Comparing Quantities CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Comparing Quantities

 S. no Terms Descriptions 1. Unitary Method Unitary Method is on the most useful method to solve ratio, proportion and percentage problems. In this we first find value of one unit and then find the value of required number of units.So in Short Unitary Method comprises two following steps:Step 1 = Find the value on one unit.Step 2 = Then find the value of required number of units. 2. Percentages Percentages are ways to compare quantities. They are numerators of fractions with denominator 100 or it basically means per 100 valuePer cent is derived Latin word ‘per centum’ meaning ‘per hundred’It is denoted by % symbol1 % means We can use either unitary method or we need to convert the fraction to an equivalent fraction with denominator 100 3. discounts Discount is a reduction given on the Marked Price (MP) of the article.This is generally given to attract customers to buy goods or to promote sales of the goods. You can find the discount by subtracting its sale price from its marked priceSo, Discount = Marked price-Sale price 4. Profit and loss Cost Price: it is the actual price of the itemOverhead charges/expenses: These additional expenses are made while buying or before selling it. These expenses have to be included in the cost priceCost price: Actual CP + overhead chargesSelling price: it is price at which the item is sold to the customerIf S. . P, We make some money from selling the item. This is called profitProfit = SP-CPProfit % If S. . P, We lose some money from selling the item. This is called lossLoss Loss % 5. Sales tax and VAT Sales tax (ST)This is the amount charged by the government on the sale of an item.It is collected by the shopkeeper from the customer and given to the government. This is, therefore, always on the selling price of an item and is added to the value of the bill.Value added tax (VAT)This is the again the amount charged by the government on the sale of an item. It is collected by the shopkeeper from the customer and given to the government. This is, therefore, always on the selling price of an item and is added to the value of the bill.Earlier you must have seen sales tax on the bill, now a day, you will mostly see value added taxCalculationIf the tax is x % , than Total after including tax would beFinal price = Cost of item 5. interest Interests the extra money paid by institutions like banks or post offices on money deposited (kept) with them. Interest is also paid by people when they borrow money 6. Simple interest Principal (P) : The original sum of money loaned/deposited. Also known as capital.Time (T) : The duration for which the money is borrowed/deposited.Rate of interest (R) : The percent of interest that you pay for money borrowed, or earn for money depositedSimple interest is calculated asTotal amount at the end of time period 7. Compound interest Principal (P) : The original sum of money loaned/deposited.Time (T) : The duration for which the money is borrowed/deposited.Rate of interest (R) : The percent of interest that you pay for money borrowed, or earn for money depositedCompound interest is the interest calculated on the previous year՚s amount

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