Ratio and Proportion (Copy)
Practice Questions — 1.11 Ratio and Proportion
Question 1
Simplify the ratios:
(a) 20 : 30 : 40
(b) 84 : 126
(c) 12 : 18 : 30
Question 2
Divide 360 in the ratio 2 : 3.
Question 3
Ali and Bilal share Rs. 840 in the ratio 5 : 2. How much does each receive?
Question 4
A recipe for 12 cookies requires 300 g of flour.
(a) How much flour is needed for 18 cookies?
(b) How much flour is needed for 5 cookies?
Question 5
On a map, the scale is 1 : 50 000.
(a) What actual distance does 4 cm represent?
(b) A road is 12 km long. How long will it appear on the map?
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 6
A car uses 18 litres of petrol to travel 270 km.
(a) How many litres are needed for 450 km?
(b) How far can the car travel on 30 litres?
Question 7
The ratio of boys to girls in a class is 7 : 5. If there are 36 students in the class, how many are boys and how many are girls?
Question 8
Two packets of biscuits cost Rs. 120 and Rs. 180. Both are the same brand and weight per rupee is proportional to size. Which is better value for money?
Question 9
Divide Rs. 2500 among A, B and C in the ratio 3 : 5 : 7.
Question 10
The angles of a triangle are in the ratio 2 : 3 : 4. Find the size of each angle.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 11
A bag contains red and blue marbles in the ratio 4 : 7. If there are 66 marbles in the bag, how many are red and how many are blue?
Question 12
In a mixture of paint, the ratio of yellow to blue is 5 : 3. If 4 litres of yellow paint are used, how much blue paint is required?
Question 13
The ratio of the sides of a rectangle is 2 : 5. If the perimeter of the rectangle is 84 cm, find the length and breadth.
Question 14
A train travels 240 km in 3 hours.
(a) How far will it travel in 5 hours at the same speed?
(b) How long will it take to travel 400 km?
Question 15
Divide 1 hour in the ratio 2 : 3. Express each share in minutes.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Answer key and explanations — 1.11 Ratio and Proportion
1.
(a) 20 : 30 : 40 → divide each by 10 → 2 : 3 : 4
(b) 84 : 126 → divide each by 42 → 2 : 3
(c) 12 : 18 : 30 → divide each by 6 → 2 : 3 : 5
Explanation: Ratios are simplified like fractions by dividing by the highest common factor.
2.
360 ÷ (2 + 3) = 360 ÷ 5 = 72
• 2 parts = 2 × 72 = 144
• 3 parts = 3 × 72 = 216
Answer: 144 and 216.
3.
Ratio = 5 : 2 → Total = 5 + 2 = 7 parts
840 ÷ 7 = 120 per part
• Ali = 5 × 120 = Rs. 600
• Bilal = 2 × 120 = Rs. 240
Answer: Ali gets Rs. 600, Bilal gets Rs. 240.
4.
12 cookies → 300 g flour
(a) 18 cookies → (18/12) × 300 = 450 g
(b) 5 cookies → (5/12) × 300 = 125 g
Answer: 450 g and 125 g.
5.
Scale = 1 : 50 000 → 1 cm = 50 000 cm = 500 m
(a) 4 cm = 4 × 500 m = 2000 m = 2 km
(b) 12 km = 12 000 m = 1 200 000 cm
Map length = 1 200 000 ÷ 50 000 = 24 cm
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
18 L → 270 km → 270 ÷ 18 = 15 km per litre
(a) 450 ÷ 15 = 30 L
(b) 30 × 15 = 450 km
Answer: 30 L and 450 km.
7.
Ratio = 7 : 5, total = 12 parts
36 ÷ 12 = 3 per part
• Boys = 7 × 3 = 21
• Girls = 5 × 3 = 15
Answer: 21 boys, 15 girls.
8.
Packet 1: Rs. 120 → 1 unit = 120
Packet 2: Rs. 180 → 1.5 units = 180 → 1 unit = 120
Answer: Both packets give the same value per unit.
9.
Ratio = 3 : 5 : 7 → total = 15 parts
2500 ÷ 15 = 166.67 per part
• A = 3 × 166.67 ≈ Rs. 500
• B = 5 × 166.67 ≈ Rs. 833
• C = 7 × 166.67 ≈ Rs. 1167
10.
Sum of ratios = 2 + 3 + 4 = 9 parts
180° ÷ 9 = 20° per part
• Angles = 40°, 60°, 80°
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
4 : 7 → total = 11 parts
66 ÷ 11 = 6 per part
• Red = 4 × 6 = 24
• Blue = 7 × 6 = 42
Answer: 24 red, 42 blue.
12.
Yellow : Blue = 5 : 3
If yellow = 5 parts → 4 litres
1 part = 4 ÷ 5 = 0.8 L
Blue = 3 × 0.8 = 2.4 L
Answer: 2.4 L blue.
13.
Sides = 2x and 5x
Perimeter = 2(2x + 5x) = 14x = 84 → x = 6
• Breadth = 2x = 12 cm
• Length = 5x = 30 cm
14.
Speed = 240 ÷ 3 = 80 km/h
(a) 5 h → 80 × 5 = 400 km
(b) 400 ÷ 80 = 5 h
Answer: 400 km, 5 h.
15.
1 hour = 60 min → ratio = 2 : 3 → total = 5 parts
60 ÷ 5 = 12 per part
• 2 parts = 24 min
• 3 parts = 36 min
Answer: 24 min and 36 min.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course