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Proportion Quiz - CBSE Class 6 Mathematics

Free practice quiz: Proportion (CBSE Class 6 Mathematics). 11 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 6 Mathematics practice quiz has 11 multiple-choice questions on Proportion, and 11 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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Ratio and Its Order

A ratio compares two quantities of the same kind by division, written a : b.
Order matters. a : b usually differs from b : a, so follow the order asked.
Simplify a ratio by dividing both terms by their common factor.

Ratio as a fraction

\[a : b = \frac{a}{b}\]

Simplest form (h is a common factor)

\[a : b = (a \div h) : (b \div h)\]

Common mistake: Writing the ratio in the wrong order, such as giving first-to-second when the question asks for second-to-first.

Proportion Means Equal Ratios

Four numbers are in proportion when the first ratio equals the second ratio.
Product of extremes equals product of means. Use this to find a missing term.

Proportion

\[a : b :: c : d \iff \frac{a}{b} = \frac{c}{d}\]

Extremes and means

\[a \times d = b \times c\]

Missing term

\[d = \frac{b \times c}{a}\]

Common mistake: Cross-multiplying the wrong pairs, or placing the two quantities in a different order in each ratio.

Unitary Method

First find the value of one unit by dividing.
Then multiply by the number of units you need.

Value of one unit

\[\text{one unit} = \frac{\text{total value}}{\text{number of units}}\]

Value of n units

\[\text{value of } n \text{ units} = n \times \text{value of one unit}\]

Common mistake: Multiplying first instead of dividing to find the value of one unit.

More Workers, Fewer Days

When more people share the same job, each person does less, so it takes fewer days.
Total work stays the same: workers multiplied by days does not change.

Same job, different team size

\[w_1 \times d_1 = w_2 \times d_2\]

New number of days

\[d_2 = \frac{w_1 \times d_1}{w_2}\]

Common mistake: Increasing the days when workers increase. More workers means fewer days for the same task.

Dividing a Total in a Ratio

Add the ratio terms to get the total number of parts.
Each share is its fraction of parts multiplied by the total amount.

Total parts

\[\text{parts} = a + b + c\]

Share of first person

\[\text{share} = \frac{a}{a + b + c} \times T\]

Value of one part

\[\text{one part} = \frac{T}{a + b + c}\]

Common mistake: Dividing the total by the number of people instead of by the sum of the ratio terms.

Exam tips

Make sure both quantities use the same units before writing a ratio.
Ask: if one quantity grows, does the other grow or shrink? Choose the method accordingly.
Check your answer: all shares should add up to the given total.

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

Sample questions

If 4 apples cost $2, how much do 12 apples cost?
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Answer: B. $6
Since 4 apples cost $2, one apple costs $0.50. Therefore, 12 apples will cost 12 * $0.50 = $6.
A recipe requires 4 cups of flour for every 3 cups of sugar. What is the proportion of flour to sugar?
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Answer: A. 4:3
The proportion can be expressed by directly taking the amounts given in the recipe as 4 cups of flour to 3 cups of sugar, which is 4:3.
A farmer has a field in the ratio of 3:5 for corn and wheat. If he grows 36 acres of corn, how much wheat does he grow?
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Answer: A. 60 acres
The ratio of corn to wheat is 3:5. If he grows 36 acres of corn (which is 3 parts), then wheat (5 parts) would be (5/3) * 36 = 60 acres.
A recipe uses 2 cups of sugar for every 3 cups of flour. If you want to use up 6 cups of sugar, how many cups of flour will you need?
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Answer: A. 9
Using the given ratio, if we use 6 cups of sugar, we need (3/2) * 6 = 9 cups of flour.
You are mixing two kinds of juice in the ratio 3:2. If you need a total of 50 liters of juice, how much of each juice do you need?
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Answer: A. 30 liters, 20 liters
Let 3x + 2x = 50. Hence, 5x = 50 gives x = 10. So, the juices required would be 3x = 30 liters and 2x = 20 liters.