Important Questions on Proportional Reasoning - 2 for Class 8

Important Questions on Proportional - 2 for Class 8 are available in this Maths article. Important Questions on Proportional - 2 for Class 8 are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Proportional - 2. Proportional - 2 helps us understand how quantities change together in different situations, which we use in everyday calculations. Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination.

Table of Contents

• Exercise 1: Inverse Proportion Questions
• Exercise 2: Time and Work Questions
• Exercise 3: Speed, Distance, and Time Questions
• MCQ Questions on Proportional Reasoning - 2
• Most Repeated Board Questions on Proportional Reasoning - 2 for Class 8

Exercise 1: Inverse Proportion Questions

Question 1: If 6 workers complete a work in 12 days, how many days will 9 workers take to complete the same work?

Solution

Workers and days are inversely proportional.

$6\times12=9\times x$

$72=9x$

$x=8$

Answer: 8 days

Question 2: A car travelling at 60 km/h takes 5 hours to cover a distance. How much time will it take at 75 km/h?

Solution

$60\times5=75\times x$

$300=75x$

$x=4$

Answer: 4 hours

Question 3: If 15 men can complete a work in 20 days, how many men are needed to complete it in 10 days?

Solution

$15\times20=x\times10$

$300=10x$

$x=30$

Answer: 30 men

Question 4: 12 machines produce goods in 8 hours. How many machines are needed to produce the same goods in 6 hours?

Solution

$12\times8=x\times6$

$96=6x$

$x=16$

Answer: 16 machines

Question 5: If 8 workers can paint a wall in 15 days, how many workers are needed to finish it in 5 days?

Solution

$8\times15=x\times5$

$120=5x$

$x=24$

Answer: 24 workers

Exercise 2: Time and Work Questions

Question 1: A worker completes a task in 18 days. How much work does he complete in 1 day?

Solution

$\frac{1}{18}$

Answer:$1/18$ of the work

Question 2: If 5 workers complete a task in 10 days, how many worker-days are required?

Solution

$5\times10=50$

Answer: 50 worker-days

Question 3: A tap fills a tank in 6 hours. What part of the tank is filled in 1 hour?

Solution

$\frac{1}{6}$

Answer:  $1/6$of the tank

Question 4: 12 labourers can finish a work in 15 days. Find the total labour-days.

Solution

$12\times15=180$

Answer: 180 labour-days

Question 5: A person completes 1/5 of a work in one day. In how many days will the work be completed?

Solution

$\frac{1}{\frac{1}{5}}=5$

Answer: 5 days

Exercise 3: Speed, Distance, and Time Questions

Question 1: A train travels 360 km in 6 hours. Find its speed.

Solution

$\frac{360}{6}=60$

Answer: 60 km/h

Question 2: Find the distance covered in 7 hours at 50 km/h.

Solution

$50\times7=350$

Answer: 350 km

Question 3: How much time will a car take to travel 240 km at 60 km/h?

Solution

$\frac{240}{60}=4$

Answer: 4 hours

Question 4: A bus travels 420 km in 7 hours. Find the speed.

Solution

$\frac{420}{7}=60$

Answer: 60 km/h

Question 5: Find the distance travelled in 9 hours at 80 km/h.

Solution

$80\times9=720$

Answer: 720 km

MCQ Questions on Proportional Reasoning - 2

Question 1: If 10 workers complete a work in 12 days, then 15 workers will complete it in:

A) 6 days
B) 8 days
C) 10 days
D) 18 days

Solution

$10\times12=15\times x$

$120=15x$

$x=8$

Answer: B) 8 days

Question 2: A car moving at 80 km/h covers a distance in 5 hours. The distance covered is:

A) 300 km
B) 350 km
C) 400 km
D) 450 km

Solution

$80\times5=400$

Answer: C) 400 km

Question 3: If 12 men complete a work in 15 days, the total man-days required are:

A) 120
B) 150
C) 180
D) 200

Solution

$12\times15=180$

Answer: C) 180

Question 4: The speed of a train travelling 540 km in 9 hours is:

A) 50 km/h
B) 55 km/h
C) 60 km/h
D) 65 km/h

Solution

$\frac{540}{9}=60$

Answer: C) 60 km/h

Question 5: If 8 workers complete a work in 20 days, how many workers are needed to complete it in 10 days?

A) 10
B) 12
C) 16
D) 20

Solution

$8\times20=x\times10$

$160=10x$

$x=16$

Answer: C) 16

Most Repeated Board Questions on Proportional Reasoning - 2 for Class 8

Question 1: Simplify the ratio 42 : 63.

Solution

$42:63=2:3$

Answer: 2 : 3

Question 2: Check whether 5, 15, 7, and 21 are in proportion.

Solution

$\frac{5}{15}=\frac{7}{21}=\frac{1}{3}$

Answer: Yes, they are in proportion.

Question 3: Find the fourth proportional to 4, 12, and 16.

Solution

Let the fourth proportional be x.

$\frac{4}{12}=\frac{16}{x}$

$4x=192$

$x=48$

Answer: 48

Question 4: If 9 notebooks cost ₹270, find the cost of 14 notebooks.

Solution

Cost of 1 notebook:

$\frac{270}{9}=30$

Cost of 14 notebooks:

$30\times14=420$

Answer: ₹420

Question 5: A car travels 360 km in 6 hours. How far will it travel in 9 hours at the same speed?

Solution

Speed per hour:

$\frac{360}{6}=60$

Distance in 9 hours:

$60\times9=540$

Answer: 540 km

Question 6: If 18 kg sugar costs ₹900, find the cost of 25 kg sugar.

Solution

Cost of 1 kg sugar:

$\frac{900}{18}=50$

Cost of 25 kg sugar:

$25\times50=1250$

Answer: ₹1250

Question 7: Find the missing term:

$6 : 9 : : 18 : 𝑥$

Solution

$\frac{6}{9}=\frac{18}{x}$

$6x=162$

$x=27$

Answer: 27

Question 8: A worker earns ₹2800 in 7 days. Find his earnings in 15 days.

Solution

Daily earning:

$\frac{2800}{7}=400$

Earning in 15 days:

$400\times15=6000$

Answer: ₹6000

Question 9: The ratio of boys to girls in a class is 3 : 4. If there are 27 boys, find the number of girls.

Solution

$\frac{3}{4}=\frac{27}{x}$

$3x=108$

$x=36$

Answer: 36 girls

Question 10: If 11 pens cost ₹176, what is the cost of 20 pens?

Solution

Cost of 1 pen:

$\frac{176}{11}=16$

Cost of 20 pens:

$20\times16=320$

Answer: ₹320

Question 11: Find the ratio of 5 hours to 20 minutes.

Solution

Convert both into minutes.

$5\text{ hours}=300\text{ minutes}$

Ratio:

$300:20=15:1$

Answer: 15 : 1

Question 12: A tap fills 240 litres of water in 8 minutes. How much water will it fill in 15 minutes?

Solution

Water filled per minute:

$\frac{240}{8}=30$

Water filled in 15 minutes:

$30\times15=450$

Answer: 450 litres

Question 13: Find whether the following ratios are equivalent:

$8:12\text{ and }14:21$

Solution

$\frac{8}{12}=\frac{14}{21}=\frac{2}{3}$

Answer: Yes, the ratios are equivalent.

Question 14: If 16 books cost ₹640, what is the cost of 30 books?

Solution

Cost of 1 book:

$\frac{640}{16}=40$

Cost of 30 books:

$30\times40=1200$

Answer: ₹1200

Question 15: A train travels 480 km in 8 hours. Find the distance travelled in 11 hours at the same speed.

Solution

Speed per hour:

$\frac{480}{8}=60$

Distance in 11 hours:

$60\times11=660$

Answer: 660 km