Important Questions Class 8 Maths Part 2 Chapter 3 Proportional Reasoning-2
Important Questions Class 8 Maths Part 2 Chapter 3 Proportional Reasoning-2
Proportional Reasoning-2 is Chapter 3 of the Class 8 Maths book Ganita Prakash Part 2. It continues the study of proportion. Students work with direct and inverse proportion, share quantities in a given ratio and solve problems on time, work and speed.
This page gives 12 important questions from Class 8 Maths Part 2 Chapter 3 Proportional Reasoning-2 with step-by-step answers prepared by Extramarks experts. The questions cover direct and inverse proportion, sharing in a ratio, map scales, and time, work and speed problems. Solve each question on paper first and then check your working with the answer.
Q1. A water-quality testing centre uses 420 ml of a reagent to test 15 samples under identical conditions.
(i) Determine the quantity of reagent required to test 28 samples.
(ii) The centre has 770 ml of the reagent available. Determine whether this quantity is sufficient and calculate the amount remaining or additionally required.
Answer: The quantity of reagent is directly proportional to the number of samples.
For 15 samples:
Reagent required per sample:
For 28 samples:
Therefore, the required quantity is:
Available quantity:
Shortage:
(i) Required reagent = 784 ml
(ii) 770 ml is not sufficient. An additional 14 ml is required.
Q2. A learning centre has 400 reward tokens divided among four categories in the ratio
the four categories are ₹2, ₹3, ₹5 and ₹8 respectively. Determine the total monetary value of all 400 tokens.
Answer: Total number of ratio parts:
Number of tokens represented by one part:
Therefore, the four categories contain:
tokens respectively.
Their monetary values are:
First category:
Second category:
Third category:
Fourth category:
Total value:
Q3. Water is distributed among three agricultural zones in the ratio 2:7:11. The largest share exceeds the smallest share by 486 litres. Determine:
(i) the total amount of water distributed
(ii) the amount received by the second zone.
Answer: Difference between the largest and smallest ratio terms:
Therefore,
One part:
Total number of parts:
Total water:
Second zone receives:
(i) Total water = 1080 litres
(ii) Second zone = 378 litres
Q4. A research fund of ₹3,780 is divided among three projects in the ratio
each project.
Answer: Convert the decimal ratio into whole numbers by multiplying every term by 4:
Total number of parts:
Value of one part:
Therefore:
First project:
Second project:
Third project:
Q5. A digital archive is divided among three storage sections in the ratio
into an equivalent whole-number ratio without changing the proportion assigned to any section.
Answer: Multiply each term by 4:
Therefore,
This can be simplified by dividing every term by 3:
Multiplying or dividing every term of a ratio by the same non-zero number does not change the relative shares.
Q6. A quantity is to be divided in the ratio
ratio, and then multiplying the quotient by 3, 7, and 8. Explain why this method is incorrect and state the correct principle for dividing the whole.
Answer:
The sum of these shares is
Hence, the sum of all ratio terms determines the number of proportional parts into which the whole is divided.
Q7. Two pipes P and Q can fill an empty cistern in 20 minutes and 30 minutes respectively. Both the pipes are opened together, but the first pipe P is turned off after some time so that the cistern is just filled in 15 minutes. After how many minutes should P be turned off?
Answer:
Q8. While driving his car at a speed of 60 km/h, Arjun reaches his office in 1 hour 40 minutes. One day, he starts 20 minutes late from home but still manages to reach on time by increasing his speed. Find the new speed of the car. Also, find the total distance covered by Arjun daily.
Answer:
Q9. 16 men can do a piece of work in 40 days. In how many days will 10 men complete the same work?
Answer:
Q10. The RF of a map is
kilometres.
Answer: 1 cm on the map represents 1,25,000 cm on the ground.
Since 1,00,000 cm = 1 km, 9,00,000 cm = 9 km.
Therefore, the geographical distance is 9 km.
Q11. 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?
Answer: Speed of car = 60 km/h, time taken = 2 hours, new speed = 80 km/h
Let the required time be x hours.
Speed and time are in inverse proportion (when speed increases, time decreases).
∴ 60 × 2 = 80 × x
⇒ 120 = 80x
⇒ x = 1.5 hours = 1 hour + 0.5 hour = 1 hour 30 minutes
Hence, the car will take 1 hour and 30 minutes to reach the destination at a speed of 80 km/h.
Q12. 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?
Answer: In 1 hour, the small pump fills 1/3 of the tank and the large pump fills 1/2 of the tank.
Together, in 1 hour they fill 1/3 + 1/2 = 2/6 + 3/6 = 5/6 of the tank.
Time taken to fill the whole tank = 1 ÷ 5/6 = 6/5 hours = 1.2 hours = 1 hour 12 minutes.
Hence, both pumps together will fill the tank in 1 hour 12 minutes.
Related Study Material on Extramarks
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Q.1 State and verify the Eulers Formula for a rectangular prism.
Marks:2
Ans
The relationship F + V = E + 2 is called the Eulers Formula.
Where, F = Number of faces, V = Number of vertices, E = Number of edges for any polyhedron
In a rectangular prism F = 6; V = 8 and E = 12
By Eulers formula, we have F + V = E + 2
F + V = 6 + 8 = 14
E + 2 = 12 + 2 = 14
F + V = E + 2
Hence, rectangular prism is a regular polyhedron.
Q.2 Which of the following is the front view of the given shape
A. 
B. 
C. 
D. 
Marks:1
Ans [ 1652275 ]
Q.3 Which of the following is not a polyhedron
A. Cylinder
B. Cube
C. Prism
D. Pyramid
Marks:1
Ans
Cylinder
Q.4 Find the number of edges, vertices and faces in a given solid.
Marks:3
Ans
Given solid is a polyhedron. There are 15 edges, 7 faces and 10 vertices in the solid.
Q.5 Draw the three views of a brick.
Marks:3
Ans
CBSE Class 8 Maths Important Questions
FAQs (Frequently Asked Questions)
The most important topics are inverse proportion, multi-term ratios, dividing a whole in a given ratio, pie charts, Representative Fraction, and direct versus inverse proportion. Inverse proportion questions on workers, pumps, speed, and time usually carry the highest marks.
Check whether the product of two quantities stays constant. If x × y remains the same and one quantity increases while the other decreases, it is inverse proportion. Workers and days, speed and time, and pumps and hours are common examples.
Add all ratio terms first. Then divide the total quantity by the sum of ratio terms to find one part. Multiply one part by each ratio term to get individual quantities. This method works for paint, concrete, coins, time division, and mixture questions.
First find the total of all values. Then calculate each sector angle using value/total × 360°. Draw each angle with a protractor and label the sector clearly. At the end, check that all sector angles add up to 360°.
Representative Fraction, or RF, is the ratio of map distance to actual ground distance written in the same unit. For example, RF 1 : 60,00,000 means 1 cm on the map represents 60,00,000 cm, or 60 km, on the ground.
Avoid treating inverse proportion as direct proportion, forgetting to add all ratio terms, adding work times instead of work rates, using wrong map scale units, and drawing pie chart sectors whose angles do not add up to 360°.