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Ratios and Percentages Quiz - CBSE Class 8 Mathematics

Free practice quiz: Ratios and Percentages (CBSE Class 8 Mathematics). 15 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 15 multiple-choice questions on Ratios and Percentages, and 15 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Ratios and Sharing in Ratios

  • A ratio compares two quantities of the same kind and unit. Simplify it by dividing both terms by their HCF.
  • To share a total in the ratio a:b, add the parts. Each share is its part over the total parts, times the total.
Simplest form (h = HCF of a and b)
\[a:b = \frac{a}{h} : \frac{b}{h}\]
First share of total T in ratio a:b
\[\frac{a}{a+b} \times T\]
Second share of total T in ratio a:b
\[\frac{b}{a+b} \times T\]
Equal ratios
\[\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc\]

Common mistake: Dividing the total by only one term of the ratio instead of by the sum of the terms (a + b).

Finding Percentages

  • Per cent means 'out of hundred'. To find what per cent a is of b, divide a by b and multiply by 100.
  • If x% of a group has one property, the remaining (100 − x)% has the other property.
x% of a quantity N
\[\frac{x}{100} \times N\]
a as a percentage of b
\[\frac{a}{b} \times 100\%\]
Whole from a part P that is x%
\[\text{Whole} = \frac{P \times 100}{x}\]

Common mistake: Dividing in the wrong order, like b ÷ a, instead of part ÷ whole when finding a percentage.

Percentage Increase and Decrease

  • Percentage change always compares the change with the original value, not with the new value.
  • After an increase of r%, the new value equals the original times (1 + r/100). Divide by this to go back.
Percentage change
\[\frac{\text{Change}}{\text{Original value}} \times 100\%\]
New value after r% increase
\[\text{New} = \text{Original} \times \left(1 + \frac{r}{100}\right)\]
Original value from increased value
\[\text{Original} = \frac{\text{New}}{1 + \frac{r}{100}}\]
New value after r% decrease
\[\text{New} = \text{Original} \times \left(1 - \frac{r}{100}\right)\]

Common mistake: Finding the original by subtracting r% of the new value. The percentage is of the original, so divide instead.

Profit and Loss

  • Cost Price (CP) is the buying price and Selling Price (SP) is the selling price. Profit happens when SP > CP.
  • Profit per cent and loss per cent are always calculated on the cost price.
Profit and loss
\[\text{Profit} = SP - CP, \quad \text{Loss} = CP - SP\]
Profit per cent
\[\text{Profit}\% = \frac{\text{Profit}}{CP} \times 100\]
SP for a profit of p%
\[SP = CP \times \left(1 + \frac{p}{100}\right)\]
SP for a loss of l%
\[SP = CP \times \left(1 - \frac{l}{100}\right)\]

Common mistake: Calculating profit per cent on the selling price instead of on the cost price.

Marked Price and Discount

  • Marked Price (MP) is the price on the tag. Discount is the reduction on the marked price.
  • Discount per cent is always on the marked price. The selling price is the price after the discount.
Discount
\[\text{Discount} = MP - SP\]
Discount per cent
\[\text{Discount}\% = \frac{\text{Discount}}{MP} \times 100\]
SP after a discount of d%
\[SP = MP \times \left(1 - \frac{d}{100}\right)\]
MP from SP after a discount of d%
\[MP = \frac{SP}{1 - \frac{d}{100}}\]

Common mistake: Subtracting the marked-up per cent and the discount per cent directly. The discount is on MP, not on CP.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. If the ratio of boys to girls in a class is 3:5, and there are 12 boys, how many girls are there?

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    Answer: B. 20

    Let the ratio of boys to girls be 3:5. If there are 12 boys, then 3x = 12, so x = 4. The number of girls is 5x = 5 * 4 = 20.

  2. Express the ratio 15:25 in its simplest form.

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    Answer: B. 3:5

    Divide both parts of the ratio by their greatest common divisor, which is 5. 15/5 = 3 and 25/5 = 5. Therefore, the simplest form is 3:5.

  3. A student scores 75 marks out of 150. What is the percentage obtained by the student?

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    Answer: B. 50%

    (75/150)*100 = 50%

  4. The population of a town increased from 5000 to 6000. What is the percentage increase in population?

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    Answer: B. 20%

    Increase in population = 6000 - 5000 = 1000. Percentage increase = (Increase/Original population) * 100 = (1000/5000) * 100 = 20%

  5. A mixture contains milk and water in the ratio 5:2. If the total quantity of mixture is 35 liters, find the quantity of milk.

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    Answer: A. 25 liters

    The ratio of milk to water is 5:2. The sum of the ratio parts is 5+2 = 7. The quantity of milk is (5/7) * 35 liters = 25 liters.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. What percentage of 50 is 25?
  2. A shop offers a 20% discount on a shirt priced at $50. What is the discounted price?
  3. If a number is increased by 15% and becomes 230, what was the original number?
  4. A fruit seller sells apples at a profit of 25%. If he bought the apples for $40, at what price does he sell them?
  5. In a school, 60% of the students are girls. If there are 120 girls, how many boys are there?
  6. A shopkeeper buys goods for $80 and sells them for $100. What is his profit percentage?
  7. Two numbers are in the ratio 2:3. If their sum is 25, find the numbers.
  8. A car is sold for $12,000 after a 15% discount. What was the original price of the car?
  9. A shopkeeper marks his goods 25% above the cost price and allows a discount of 10%. What is his profit percentage?
  10. The length and breadth of a rectangle are in the ratio 3:2. If the perimeter is 50 cm, find the area of the rectangle.

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