Short Questions
1. What is the simplest form of the ratio 18 : 24?
Solution:
HCF of 18 and 24 = 6
Divide both terms by 6
18 ÷ 6 : 24 ÷ 6 = 3 : 4
2. Are 4 : 6 and 8 : 12 proportional?
Solution:
4 : 6 = 2 : 3
8 : 12 = 2 : 3
Both are same, so proportional.
3. Find the missing number: 5 : 10 :: 15 : ?
Solution:
5 × 3 = 15
10 × 3 = 30
4. Divide ₹300 in the ratio 1 : 2.
Solution:
Total parts = 1 + 2 = 3
₹300 ÷ 3 = ₹100
Parts = ₹100 and ₹200
5. Write 40 : 20 in simplest form.
Solution:
Divide by 20
40 ÷ 20 : 20 ÷ 20 = 2 : 1
6. If 6 notebooks cost ₹60, what is cost of 1 notebook?
Solution:
60 ÷ 6 = ₹10
7. Convert 3 litres into mL.
Solution:
1 litre = 1000 mL
3 × 1000 = 3000 mL
8. Find the ratio of 15 cm to 45 cm.
Solution:
Divide both by 15
15 : 45 = 1 : 3
9. Are 2 : 5 and 6 : 15 proportional?
Solution:
2 : 5 = 6 : 15
Both multiplied by 3
10. What is HCF of 12 and 16?
Solution:
Factors of 12 = 1,2,3,4,6,12
Factors of 16 = 1,2,4,8,16
Highest common factor = 4
Long Questions
1. Divide ₹4500 in the ratio 2 : 3.
Solution:
Total parts = 2 + 3 = 5
₹4500 ÷ 5 = ₹900
First part = 2 × 900 = ₹1800
Second part = 3 × 900 = ₹2700
2. Acid and water are mixed in ratio 1 : 5. Find acid and water in 240 mL solution.
Solution:
Total parts = 1 + 5 = 6
240 ÷ 6 = 40
Acid = 1 × 40 = 40 mL
Water = 5 × 40 = 200 mL
3. Blue and yellow paints are mixed in ratio 3 : 5 to make 40 mL paint. Find quantity of each color.
Solution:
Total parts = 3 + 5 = 8
40 ÷ 8 = 5
Blue = 3 × 5 = 15 mL
Yellow = 5 × 5 = 25 mL
4. A tap fills 500 mL mug in 15 seconds. How much time for 10 litre bucket?
Solution:
10 litre = 10000 mL
10000 ÷ 500 = 20 mugs
20 × 15 = 300 seconds
5. 6 glasses lemonade need 10 spoons sugar. How many spoons for 18 glasses?
Solution:
6 × 3 = 18
10 × 3 = 30
So sugar needed = 30 spoons
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