ANSWERs for figure it out Class 8 Mathematics – NCERT (Ganita Prakash) Part 2 Chapter 3: PROPORTIONAL REASONING–2

 ANSWERs for figure it out Class 8 Mathematics – NCERT (Ganita Prakash) Part 2  

Chapter 3: PROPORTIONAL REASONING–2 

Example 1: 

To make a special shade of purple, paint must be mixed in the ratio, Red : Blue : White :: 2 : 3 : 5. If Yasmin has 10 litres of white paint, how many litres of red and blue paint should she add to get the same shade of purple? 

In the ratio 2 : 3 : 5, the white paint corresponds to 5 parts. If 5 parts is 10 litres, 1 part is 10 ÷ 5 = 2 litres. Red = 2 parts = 2 × 2 = 4 litres. 

Blue = 3 parts = 3 × 2 = 6 litres. 

So, the purple paint will have 4 litres of red, 6 litres of blue, and 10 litres of white paint. 

What is the total volume of this purple paint?

 The total volume of purple paint is 4 + 6 + 10 = 20 litres.

Example 2: 

Cement concrete is a mixture of cement, sand, and gravel, and is widely used in construction. The ratio of the components in the mixture varies depending on how strong the structure needs to be. For structures that need greater strength like pillars, beams, and roofs, the ratio is 1 : 1.5 : 3, and the construction is also reinforced with steel rods. Using this ratio, if we have 3 bags of cement, how many bags of concrete mixture can we make? 

The concrete mixture is in the ratio Bags of cement : bags of sand : bags of gravel :: 1 : 1.5 : 3. 

If we have 3 bags of cement, we have to multiply the other terms by 3. 

So, the ratio is cement : sand : gravel :: 3 : 4.5 : 9. 

In total, we have 3 + 4.5 + 9 = 16.5 bags of concrete

Figure it Out Page number 60

1. A cricket coach schedules practice sessions that include different activities in a specific ratio — time for warm-up/cool-down : time for batting : 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?

Question 1: Cricket Practice Session

Given: Ratio of time = 3 : 4 : 3 : 5, Total time = 150 minutes

Step 1: Add ratio terms 3 + 4 + 3 + 5 = 15

Step 2: Find value of 1 part 150 ÷ 15 = 10 minutes

Step 3: Calculate time for each activity

• Warm-up/Cool-down = 3 × 10 = 30 minutes

• Batting = 4 × 10 = 40 minutes

• Bowling = 3 × 10 = 30 minutes

• Fielding = 5 × 10 = 50 minutes

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?

Question 2: Library Books

Given: Odiya : Hindi : English = 3 : 2 : 1, Odiya books = 288

Step 1: Value of 1 part 288 ÷ 3 = 96

Step 2: Find other quantities

• Hindi books = 2 × 96 = 192

• English books = 1 × 96 = 96

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?

Question 3: Coins Problem

Given: Coin ratio = 4 : 3 : 2 : 1, Total coins = 100

Step 1: Sum of ratio = 10

Step 2: Value of 1 part 100 ÷ 10 = 10

Step 3: Number and value of coins

• ₹10 coins = 40 → ₹400

• ₹5 coins = 30 → ₹150

• ₹2 coins = 20 → ₹40

• ₹1 coins = 10 → ₹10

Total money = ₹600

 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? 

Question 4: Triangle with sides 3 : 4 : 5

Answer: Yes, such a triangle can be constructed.

Explanation: 3 + 4 > 5, 4 + 5 > 3, 3 + 5 > 4

All triangle inequalities are satisfied.

Congruency: All such triangles are not congruent, but similar, because actual side lengths may differ.

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

Question 5: Triangle with sides 1 : 3 : 5

Answer: Cannot be constructed.

Reason: 1 + 3 = 4 < 5

This violates the triangle inequality rule.

Figure it Out Page number 62

1. A group of 360 people were asked to vote for their favourite season from the three seasons — rainy, winter and summer. 90 liked the summer season, 120 liked the rainy season, and the rest liked the winter. Draw a pie chart to show this information. 

Question 1: Favourite Seasons

Given

Total number of people = 360

• Summer = 90

• Rainy = 120

• Winter = 360 − (90 + 120) = 150

Season	Number of People
Summer	90
Rainy	120
Winter	150
Total	360

Find the angle for each sector

Total angle of a circle = 360°

Formula used:

$$\text{Angle} = \frac{\text{Number of people}}{\text{Total people}} \times 360^\circ$$

Summer

$$\frac{90}{360} \times 360^\circ = 90^\circ$$

Rainy

$$\frac{120}{360} \times 360^\circ = 120^\circ$$

Winter

$$\frac{150}{360} \times 360^\circ = 150^\circ$$

Draw the Pie Chart (Construction Steps)

1. Draw a circle with centre O.

2. Draw a radius OA.

3. Using a protractor:

   • Measure 90° from OA and draw radius OB → Summer

   • From OB, measure 120° and draw radius OC → Rainy

   • The remaining sector (150°) represents Winter

5. Summer → 90 people → 90°

6. Rainy → 120 people → 120°

7. Winter → 150 people → 150°

8. Label each sector clearly.

9. Shade or colour each sector differently.

10. 
    
    
    

2. Draw a pie chart based on the following information about viewers᾿ favourite type of TV channel: Entertainment — 50%, Sports — 25%, News — 15%, Information — 10%.  

3. Prepare a pie chart that shows the favourite subjects of the students in your class. You can collect the data of the number of students for Proportional Reasoning–2 each subject shown in the table (each student should choose only one subject). Then write these numbers in the table and construct a pie chart: