Get the simplified Class 8 Maths Extra Questions Part 2 Chapter 3 Proportional Reasoning 2 Class 8 Extra Questions and Answers with complete explanation.
Class 8 Proportional Reasoning 2 Extra Questions
Class 8 Maths Chapter 3 Proportional Reasoning 2 Extra Questions
Proportional Reasoning 2 Extra Questions Class 8
Very Short Answer Type Questions
Question 1.
Divide 360 in the ratio 2 : 4 : 6.
Answer:
Sum of ratio terms = 2 + 4 + 6 = 12
Now, 1 part = 360 + 12 = 30
Then, the parts are
2 × 30 = 60, 4 × 30 = 120 and 6 × 30 = 180
So, the parts are 60,120 and 180
Question 2.
If 5 notebooks cost ₹ 150, what is the cost of 8 notebooks?
Answer:
Given, Number of notebooks = 5 and cost = ₹ 150
Now, number of notebooks = 8
Let required cost = ₹ x
Here, cost increases, when quantity increases, so it is a direct proportion.
So, 5 : 8 :: 150 : x
Using direct proportion rules, we get
x = \(\frac{150 \times 8}{5}\)
⇒ x = \(\frac{1200}{5}\) = 240
Hence, the cost of 8 notebooks = ₹ 240.
Question 3.
6 workers complete a job in 10 days. How many days will 3 workers take?
Answer:
Given, workers = 6 and days = 10
Now, workers = 3
Let required days = x
If number of workers decreases, the time taken increases. So, it is an inverse proportion.
So, 6 × 10 = 3 × x
⇒ 60 = 3x
⇒ x = \(\frac{1}{2}\) =20
Hence, 3 workers will take 20 days.
Question 4.
On a map with scale 1:100000, the distance between two towns is 3 cm. Find the actual distance.
Answer:
Scale = 1 : 1000000
Map distance = 3 cm
This means, 1 cm on map = 100000 cm in actual distance.
So, for 3cm,
3 × 100000 = 300000 cm
On converting into metres, we get
300000 + 100 = 3000 metres
On converting into kilometres,
we get 3000 + 1000 = 3 km
Hence, the actual distance =3 km.
Question 5.
Construct a triangle, whose angles are in the ratio 6 : 8 :10.
Answer:
Given, the sum of angles in a triangle is 180° and the ratio of angles is 6:8:10.
Let the common multiplier be x.
Then, 6x + 8x + 10x = 180
⇒ 24x = 180
⇒ x = \(\frac{180}{24}\)
x = 7.5
Now, the angles are,
6x = 6 × 7.5 = 45°,
8x = 8 × 7.5 = 60p
and 10x = 10 × 7.5 = 75°
Short Answer Type Question
Question 1.
Fill in the empty cells if x and y are in inverse proportion.
Answer:
Given, x and y are in inverse proportion.
So, x × y = constant
Using the first complete pair,
we get x × y = 18 × 20 =360
So, x × y = 360
(i) When x = 12
y = \(\frac{360}{12}\) = 30
(ii) When x = 30
y = \(\frac{360}{30}\) = 12
(iii) When x = 36
y = \(\frac{360}{36}\) = 10
Hence, the missing values are 30,12, and 10.
Question 2.
A fitness trainer divides an exercise session among different activities in the ratio, stretching: strength training: cardio : cool-down :: 2 : 3 : 4 :1.
If each session lasts 120 minutes, how much time is spent on each activity?
Answer:
Total ratio = 2 + 3 + 4 + 1 = 10
Value of 1 part = \(\frac{120}{10}\) = 12 mm
So, stretching =2 × 12 = 24 min
Strength training = 3 × 12 = 36 min
Cardio = 4 × 12 = 48 min
CooTdown = 1 × 12 = 12 min
Question 3.
A person has 150 currency notes in the ratio:
₹ 100 notes: ₹ 50 notes: ₹ 20 notes: ₹ 10 notes :: 2 : 3 : 1 : 4
Find the total amount of money.
Answer:
Given, ratio,
₹ 100 notes : ₹ 50 notes : ₹ 20 notes : ₹ 10 notes :: 2 : 3 : 1 : 4
Now, total ratio = 2 + 3 + 1 + 4 = 10
1 part = \(\frac{150}{10}\) = 15 notes 10
Then, number of notes,
₹ 100 notes = 2 × 15 = 30 notes
₹ 50 notes = 3 × 15 = 45 notes
₹ 20 notes = 1 × 15 = 15 notes
₹ 10 notes = 4 × 15 = 60 notes
So, total money = 30 × 100+ 45 × 50 + 15 × 20+ 60 × 10
= 3000 + 2250 + 300 + 600
= ₹ 6150
Question 4.
The pie chart shows how a student divides study time among three subjects in a day.
If the student studies for 4 hours in total, answer.
(i) How much time is spent on Science?
Answer:
Since, total central angle of pie chart is 360°.
So, traction for Science = \(\frac{150}{360}=\frac{5}{12}\)
Total time = 4h
So, time spent on Science = \(\frac{5}{12}\) × 4 = \(\frac{20}{12}=\frac{5}{3}\) = 1\(\frac{2}{3}\) = h 40 min
(ii) Which subject gets the least study time?
Answer:
From the pie chart, smallest angle = 90° (English)
So, English gets the least study time.
Long Answer Type Questions
Question 1.
A pie chart shows the modes of transport used by students to reach a coaching centre.
Answer the following questions.
(i) Which is the most commonly used mode of transport?
Answer:
From the pie chart,
Largest angle = 140° (Bus)
So, Bus is the most common mode.
(ii) What fraction of students travel by bicycle?
Answer:
The angle for bicycle is 40°.
Then, fraction travelling by bicycle = \(\frac{40^{\circ}}{360^{\circ}}=\frac{1}{9}\)
(iii) If 14 students travel by car, how many students were surveyed in total?
Answer:
Car angle = 40°
Now, fraction for car = \(\frac{40^{\circ}}{360^{\circ}}=\frac{1}{9}\)
So, total students =14 × 9 = 126 students
(iv) Which two modes of transport are used by equal number of students?
Answer:
From the pie chart, equal angles = Bicycle (40°) and Car (40°)
Hence, equal number of students use bicycle and car.
Question 2.
Six workers can complete a piece of work in 15 days, working for equal hours each day.
(i) How many days will 10 workers take to complete the same work?
Answer:
Workers and days are in inverse proportion.
So, Workers × Days = constant
Let the number of days be x.
So, 6 × 15 = 10 × x
⇒ x = \(\frac{90}{10}\) = 9
Hence, 10 workers will take 9 days.
(ii) If only 5 workers are available, how many days will the work take?
Answer:
Let the number of days be y.
So, 6 × 15 = 5 × y
⇒ y = \(\frac{90}{5}\) = 18
Hence, 5 workers will take 18 days
(iii) State the assumptions made in this problem.
Answer:
Assumptions
All workers work with the same efficiency.
All workers work for equal hours daily.
No worker joins or leaves during the work.
Skill Based Questions
Question 1.
A car travels a fixed distance at 40 km/h in 5 h. How long will it take to cover the same distance at 50 km/h?
Answer:
4 hours
Question 2.
The ratio of ₹ 10, ₹ 5 and ₹ 2 coins in a bag is 3 : 4: 5. If there are 120 coins in total, find the total value of coins.
Answer:
₹ 600
Question 3.
Two sambar recipes are
Recipe A 4 cups water: 2 cups dal: 1 cup vegetables Recipe B 10 cups water: 5 cups dal: 2.5 cups vegetables
(a) Are the recipes proportional?
Answer:
Yes
(b) Will the taste (thickness) be similar if cooked similarly?
Answer:
Yes
Question 4.
A spice mix uses : coriander: chilli: toor dal: methi = 8 : 4 : 2 :1. Puneet wants to make a smaller batch with 3 spoons of coriander.
(a) Find the required amounts of chilli, toor dal and methi to get the same taste.
Answer:
Chilli = 1.5 spoons,
Toor dal = 0.75 spoons and Methi = 0.375 spoons
(b) Write the new ratio.
Answer:
3:1.5:3.75:0375
Question 5.
A tank is being filled by identical taps.
Is time inversely proportional to number of taps?
Answer:
Yes
Case Study Based Questions
Question 1.
A newly opened bakery shop makes three types of cookies—Chocolate, Butter and Oats cookies.
Answer:
(i) Given, Ratio = 5 : 3 : 2 (Chocolate : Butter : Oats),
Total = 2000 cookies
On adding the ratio terms,
we get 5 + 3 + 2 = 10
So, number of chocolate cookies = 2000 × \(\frac{5}{10}\) = 1000
Number of butter cookies =2000 × \(\frac{3}{10}\) = 600
Number of oats cookies =2000 × \(\frac{2}{10}\) = 400
Hence, 1000 chocolates, 600 butter and 400 oats cookies were sold in the first week.
(ii) 20% increase means, we multiply by 1.2
So, chocolate cookies =1000 × 1.2 = 1200
butter = 600 × 1.2 =720
oats cookies = 400 × 1.2 = 480
Hence, 1200 chocolate, 720 butter and 480 oats cookies were sold in the second week.
(iii) Total cookies sold in the second week
= 1200 + 720 + 480
= 2400
(iv) Increase in cookies = The number of in cookies sold in second week – The number of in cookies sold in first week
= 2400 – 2000
= 400 cookies [from part c]
Hence, the total sales increased by 400 cookies in the second week.