The document Points to Remember- Comparing Quantities Class 8 Notes | EduRev is a part of the Class 8 Course Mathematics (Maths) Class 8.

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**Points to Remember**** **

- For profit, SP > CP and for loss, CP > SP.
- Profit or loss is always calculated on CP.
- The overhead expenses are a part of CP.
- Discount is always calculated on the marked price.
- VAT is not a part of selling price. Of course it is calculated on selling price but it is excluded from the SP while calculating profit or loss.
- Formula for compound interest gives,

Amount =

Then CI = A – P.

- If the interest is compounded half yearly the time period becomes twice as much as the number of years.The rate of interest is reduced to half.

**We Know That**

We compare two quantities by division. Comparing by division is called ratio. Quantities written in ratio have the same units. Ratio has no unit. Two equal ratios are said to form a proportion. In a proportion, product of extremes is equal to the product of the means.

Another way of comparing quantities is to express them as percentages. Percentage means hundredth. It is the numerator of a fraction with denominator 100. To convert ratio into pe cent, we convert it into a fraction with denominator as 100. In unitary method, we find the value for one (i.e. for a unit) and then find the value of many.**Solved Examples:Question 1: In a survey of 50 students, 80% of students liked Science, and 20% of students liked Arts. How many numbers of students liked Science?Solution: **We know that 80% of students liked science in the survey of 50 students

∴ Number of students who liked Science = 80/100 × 50 = 40

Solution:

Death rate (%) in 2016 = 35/210 × 100 = 16.66%

Death rate (%) in 2017 = 10/150 × 100 = 6.66%

Clearly, there is a decrease in death rate in the hospital in 2017 when compared to that in 2016.

∴ Decrease in death rate (%) = (16.66−6.66)/100 × 100 = 10%

**Question 3: The value of a residential flat constructed at a cost of Rs100000 is depreciating at the rate of 10% per annum. What will be its value 3 years after construction?Solution: **We have: V0= Initial value= Rs 100000, R= Rate of depreciation = 10% per annum, n = 3 years. Therefore: Value after n years,

after putting value of n and R, we get:

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