Important Questions (Practical) Class 8 Maths Ganita Prakash – II Chapter 3 Proportional Reasoning-2

Short Practical Questions

Question: Map scale = 1 : 60,00,000. Distance on map = 1 cm. Find real distance.

Steps:

1. 1 cm = 60,00,000 cm
2. Convert → 60 km

Answer: 60 km

Question: Scale 1 : 50. Drawing length = 3 cm. Find actual length.

Steps:

1. Actual = 3 × 50
2. = 150 cm

Answer: 150 cm

Question: Ratio 2 : 3. Total = 50. Find both parts.

Steps:

1. Sum = 5
2. One part = 50 ÷ 5 = 10
3. Parts = 20 and 30

Answer: 20, 30

Question: Ratio 4 : 5. If first part = 20, find second part.

Steps:

1. Factor = 20 ÷ 4 = 5
2. Second part = 5 × 5 = 25

Answer: 25

Question: Ratio 2 : 3 : 5. Total = 40. Find first part.

Steps:

1. Sum = 10
2. One part = 40 ÷ 10 = 4
3. First part = 2 × 4 = 8

Answer: 8

Question: 2 pumps fill tank in 12 hours. Time with 4 pumps?

Steps:

1. Inverse proportion
2. 2 × 12 = 4 × x
3. x = 6

Answer: 6 hours

Question: Speed = 40 km/h, time = 2 h. If speed = 80 km/h, find time.

Steps:

1. Speed doubles → time halves
2. 2 ÷ 2 = 1

Answer: 1 hour

Question: Total students = 20. Students in group A = 5. Find angle.

Steps:

1. Angle = (5/20) × 360
2. = 1/4 × 360
3. = 90°

Answer: 90°

Question: Ratio 3 : 2 : 1. Total = 60. Find smallest part.

Steps:

1. Sum = 6
2. One part = 60 ÷ 6 = 10
3. Smallest = 1 × 10

Answer: 10

Question: 5 workers do a job in 4 days. Days for 1 worker?

Steps:

1. Inverse proportion
2. 5 × 4 = 1 × x
3. x = 20

Answer: 20 days

Long Practical Questions

Question: A map has a scale of 1 : 60,00,000. The distance between two cities on the map is 4 cm. Find the actual distance.

Steps:

1. Scale means 1 cm on map = 60,00,000 cm in reality
2. Convert to km:
   60,00,000 cm = 60 km
3. For 4 cm:
   4 × 60 = 240 km

Answer: 240 km

Question: Divide 90 in the ratio 2 : 3 : 4.

Steps:

1. Add ratio parts:
   2 + 3 + 4 = 9
2. Find one part:
   90 ÷ 9 = 10
3. Multiply each:
   2 × 10 = 20
   3 × 10 = 30
   4 × 10 = 40

Answer: 20, 30, 40

Question: Paint is mixed in the ratio 2 : 3 : 5. Total paint needed = 100 litres. Find each part.

Steps:

1. Total ratio = 2 + 3 + 5 = 10
2. One part = 100 ÷ 10 = 10
3. Calculate:
   Red = 2 × 10 = 20 L
   Blue = 3 × 10 = 30 L
   White = 5 × 10 = 50 L

Answer:
Red = 20 L, Blue = 30 L, White = 50 L

Question: 15 workers complete a job in 6 days. How many days will 10 workers take?

Steps:

1. Workers ↓ → Days ↑ (inverse proportion)
2. Use formula:
   15 × 6 = 10 × x
3. Solve:
   90 = 10x
   x = 9

Answer: 9 days

Question:
Total students = 40
Students with Grade A = 10
Find the angle for Grade A in a pie chart.

Steps:

1. Formula:
   Angle = (Part / Total) × 360°
2. Substitute values:
   = (10 / 40) × 360
3. Solve:
   = 1/4 × 360
   = 90°

Answer: 90°