Question 1

A cricket coach schedules practice sessions that include different activities in a specific ratio — time for warm-up/cool-down: time for hatting: time for bowling: time for fielding:: 3 : 4 : 3 : 5. If each session is 150 minutes long, how much time is spent on each activity?

Accepted Answer

Given, time for warm-up/cool-down : time for batting : Time for bowling : time for fielding :: 3 : 4 : 3 : 5
Total number of ratio parts = 3 + 4 + 3 + 5 = 15
Total time of each session = 150 minutes
So, time for warm-up/cool-down = $\frac {3}{15}$ × 150 = 30 minutes
Time for batting = $\frac {4}{15}$ × 150 = 40 minutes
Time for bowling = $\frac {3}{15}$ × 150 = 30 minutes
Time for fielding = $\frac {5}{15}$ × 150 = 50 minutes
Verification: 30 + 40 + 30 + 50 = 150 minutes

Question 2

A school library has books in different languages in the following ratio — no. of Odiya books : no. of Hindi books : no. of English books :: 3 : 2 : 1. If the library has 288 Odiya books, how many Hindi and English books does it have?

Accepted Answer

Given, No. of Odiya books : No. of Hindi books : No. of English books :: 3 : 2 : 1
Let x be the total number of books.
No. of Odiya books = $\frac {3}{6}$ × x
⇒ 288 = $\frac {3}{6}$ × x
⇒ x = 576
∴ No. of Hindi books = $\frac {2}{6}$ × 576 = 192
and no. of English books = $\frac {1}{6}$ × 576 = 96

Question 3

I have 100 coins in the ratio — no. of ₹ 10 coins : no. of ₹ 5 coins : no. of ₹ 2 coins : no. of ₹ 1 coins :: 4 : 3 : 2 : 1. How much money do I have in coins?

Accepted Answer

Given no. of ₹ 10 coins : no. of ₹ 5 coins : no. of ₹ 2 coins : no. of ₹ 1 coins :: 4 : 3 : 2 : 1.
Total number of coins = 100
Total number of ratio parts = 4 + 3 + 2 + 1 = 10
no. of ₹ 10 coins = $\frac {4}{10}$ × 100 = 40
no. of ₹ 5 coins = $\frac {3}{10}$ × 100 = 30
no. of ₹ 2 coins = $\frac {3}{10}$ × 100 = 30
no. of ₹ 1 coins = $\frac {1}{10}$ × 100 = 10
Total money = 40 × 10 + 30 × 5 + 2 × 20 + 1 × 10
= 400 + 150 + 40 + 10
= ₹ 600

Question 4

Construct a triangle with sidelengths in the ratio 3 : 4 : 5. Will all the triangles drawn with this ratio of sidelengths be congruent to each other? Why or why not?

Accepted Answer

We can construct triangles with sides in the ratio 3 : 4 : 5.
They will not be congruent to each other.
Reason:
Triangle 1: Let sides 3 cm, 4 cm, 5 cm
Triangle 2: Let sides 6 cm, 8 cm, 10 cm
Triangle 3: Let sides = 9 cm, 12 cm, 15 cm
Though all these triangles have the same ratio (3 : 4 : 5), their actual sizes are different.
Congruent triangles must have the same shape and size.
These triangles have the same shape (they are similar) but different sizes.
Hence, they are not congruent.

Question 5

Can you construct a triangle with sidelengths in the ratio 1 : 3 : 5? Why or why not?

Accepted Answer

For a triangle to exist, it must satisfy the triangle inequality theorem, which states:
The sum of any two sides of a triangle must be greater than the third side.
Let’s take
Side 1 = 1 cm
Side 2 = 3 cm
Side 3 = 5 cm
1. 1 + 3  5 (No)
2. 1 + 5 > 3 ⇒ 6 > 3 (Yes)
3. 3 + 5 > 1 ⇒ 8 > 1 (Yes)
Since the first condition fails (1 + 3 = 4

Question 6

Three workers can paint a fence in 4 days. If one more worker joins the team, how many days will it take them to finish the work? What are the assumptions you need to make?

Accepted Answer

When the number of workers increases, the number of days needed to paint the fence decreases.
Assumptions Needed
(i) All workers work at the same speed/rate.
(ii) The work is uniformly distributed among all workers.
(iii) All workers work for the same number of hours each day.
So, the number of workers and the number of days are in inverse proportion.
Let x be the no. of days taken.
3 × 4 = 4 × x
⇒ x = 3
So, they will take 3 days to finish the work.

Question 7

It takes 6 hours to fill 2 tanks of the same size with a pump. How long will it take to fill 5 such tanks with the same pump?

Accepted Answer

No. of hours and no. of tanks are in direct proportion.
Let 5 such tanks take x hours.
$\frac{6}{2}=\frac{x}{5}$
⇒ x = 15
So, 5 tanks will take 15 hours.

Source: This question is from Proportional Reasoning 2, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Proportional Reasoning 2: Takes, Hours, Fill, Tanks, Same, Size. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
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Q2: A school library has books in different languages in the following ratio — no. of Odiya books : no....
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Question 8

A given set of chairs is arranged in 25 rows, with 12 chairs in each row. If the chairs are rearranged with 20 chairs in each row, how many rows does this new arrangement have?

Accepted Answer

No. of rows and no. of chairs in each row are in inverse proportion.
Let the new arrangement have x rows.
25 × 12 = x × 20
⇒ x = 15
So, the new arrangement has 15 rows.

Source: This question is from Proportional Reasoning 2, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Proportional Reasoning 2: Set, Chairs, Arranged, Rows, Row, Rearranged. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Proportional Reasoning 2Q1: A cricket coach schedules practice sessions that include different activities in a specific ratio —...
Q10: A small pump can fill a tank in 3 hours, while a large pump can fill the same tank in 2 hours. If...
Q12: A car takes 2 hours to reach a destination, travelling at a speed of 60 km/h. How long will the car...
Q2: A school library has books in different languages in the following ratio — no. of Odiya books : no....
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Question 9

A school has 8 periods a day, each of 45 minutes duration. How long is each period, if the school has 9 periods a day, assuming that the number of school hours per day stays the same?

Accepted Answer

No. of periods and the duration of each period are in inverse proportion.
Let each period be of x minutes.
8 × 45 = 9 × x
⇒ x = 40
So, each period is 40 minutes.

Source: This question is from Proportional Reasoning 2, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Proportional Reasoning 2: School, Periods, Day, Minutes, Duration, Long. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Proportional Reasoning 2Q1: A cricket coach schedules practice sessions that include different activities in a specific ratio —...
Q10: A small pump can fill a tank in 3 hours, while a large pump can fill the same tank in 2 hours. If...
Q12: A car takes 2 hours to reach a destination, travelling at a speed of 60 km/h. How long will the car...
Q2: A school library has books in different languages in the following ratio — no. of Odiya books : no....
Q3: I have 100 coins in the ratio — no. of ₹ 10 coins : no. of ₹ 5 coins : no. of ₹ 2 coins : no. of ₹...
Practice more questions from Proportional Reasoning 2 &mdash; Mathematics, Class 8 CBSE

Question 10

A small pump can fill a tank in 3 hours, while a large pump can fill the same tank in 2 hours. If both pumps are used together, how long will the tank take to fill?

Accepted Answer

Let x litres be the capacity of the tank.
Then, water filled by small tank in one hour = $\frac {x}{3}$ litre
Water filled by large tank in one hour = $\frac {x}{2}$ litre
So, total water filled by both pumps in one hour = $\left(\frac{x}{3}+\frac{x}{2}\right)$ litre = $\frac {5x}{6}$ litre
∴ Time taken by both pumps used together to fill the tank = $\left(1 \div \frac{5 x}{6}\right) \times x$
= 1 × $\frac {6}{5x}$ × x
= $\frac {6}{5}$ hour
= 1$\frac {1}{5}$ hour

Question 11

A factory requires 42 machines to produce a given number of toys in 63 days. How many machines are required to produce the same number of toys in 54 days?

Accepted Answer

No. of machines and no. of days are in inverse proportion.
42 × 63 = x × 54
⇒ x = 49
So, 49 machines are required.

Source: This question is from Proportional Reasoning 2, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Proportional Reasoning 2: Factory, Requires, Machines, Produce, Number, Toys. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Proportional Reasoning 2Q1: A cricket coach schedules practice sessions that include different activities in a specific ratio —...
Q10: A small pump can fill a tank in 3 hours, while a large pump can fill the same tank in 2 hours. If...
Q12: A car takes 2 hours to reach a destination, travelling at a speed of 60 km/h. How long will the car...
Q2: A school library has books in different languages in the following ratio — no. of Odiya books : no....
Q3: I have 100 coins in the ratio — no. of ₹ 10 coins : no. of ₹ 5 coins : no. of ₹ 2 coins : no. of ₹...
Practice more questions from Proportional Reasoning 2 &mdash; Mathematics, Class 8 CBSE

Question 12

A car takes 2 hours to reach a destination, travelling at a speed of 60 km/h. How long will the car take if it travels at a speed of 80 km/h?

Accepted Answer

Let the car take t hours.
The speed of the car and the time taken are in inverse proportion.
So, 2 × 60 = t × 80
⇒ t = 1.5 hour
So, the car will take 1.5 hours.

Source: This question is from Proportional Reasoning 2, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Proportional Reasoning 2: Car, Takes, Hours, Reach, Destination, Travelling. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Proportional Reasoning 2Q1: A cricket coach schedules practice sessions that include different activities in a specific ratio —...
Q10: A small pump can fill a tank in 3 hours, while a large pump can fill the same tank in 2 hours. If...
Q2: A school library has books in different languages in the following ratio — no. of Odiya books : no....
Q3: I have 100 coins in the ratio — no. of ₹ 10 coins : no. of ₹ 5 coins : no. of ₹ 2 coins : no. of ₹...
Q4: Construct a triangle with sidelengths in the ratio 3 : 4 : 5. Will all the triangles drawn with...
Practice more questions from Proportional Reasoning 2 &mdash; Mathematics, Class 8 CBSE