Ratio and Proportion

Short Answer Questions(SAQs)

What is the ‘Golden ratio’?

Two numbers are in the golden ratio if the ratio of the sum of the numbers (a + b) to the larger number (a) is the same as the ratio of the larger number (a) to the smaller number (b), i.e., a + ba = ab.

What is known as the ‘Unitary method’?

The unitary method is a process of finding the value of a single unit. Based on this value, the value of the required number of units is found.

What is meant ‘Fraction’?

A fraction represents a part of a whole or, more generally, any number of equal parts.

MCQs

1. What is the ratio of 4 to 8?

(a) 1:2

(b) 2:1

(c) 4:4

(d) 8:1

► (a) 48 simplifies to 1:2.

2. Which of the following represents a proportion?

(a) 2:3 = 4:6

(b) 1:2 = 2:5

(c) 3:4 = 6:9

(d) 1:3 = 3:5

► (a) 2:3 and 4:6 are equivalent ratios.

3. The ratio 5:10 is equal to:

(a) 1:3

(b) 1:2

(c) 2:5

(d) 3:5

► (b) 5:10 = 1:2.

4. 12 pens and 8 pencils are in the ratio:

(a) 2:3

(b) 3:2

(c) 3:4

(d) 4:3

► (b) 128 = 3:2.

5. 3:5 = x:20, find x.

(a) 12

(b) 10

(c) 8

(d) 15

► (d) Cross multiply: 3 × 20 = 5 × x ⇒ x = 12.

6. Which is the simplest form of 18:27?

(a) 6:9

(b) 2:3

(c) 3:4

(d) 9:6

► (b) Divide both terms by 9 ⇒ 2:3.

7. If 10 notebooks cost ₹150, cost of 1 notebook is:

(a) ₹10

(b) ₹12

(c) ₹15

(d) ₹25

► (b) 15010 = ₹15.

8. 1 dozen = 12 items. Then 5 dozen =

(a) 50

(b) 60

(c) 70

(d) 12

► (b) 5 × 12 = 60.

9. The ratio 7:21 is equivalent to:

(a) 1:2

(b) 1:3

(c) 3:1

(d) 7:1

► (b) 721 = 1:3.

10. What is the ratio of 25 paise to ₹1?

(a) 1:3

(b) 1:2

(c) 1:4

(d) 4:1

► (c) 25100 = 1:4.

11. If a:b = 2:5 and b:c = 4:3, then a:b:c =

(a) 8:20:15

(b) 2:5:3

(c) 2:4:3

(d) 2:5:4

► (a) LCM of b = 20 ⇒ a:b:c = 8:20:15.

12. What is 25% of 200?

(a) 25

(b) 50

(c) 75

(d) 100

► (b) 25100 × 200 = 50.

13. The terms in a ratio are always:

(a) Equal

(b) Same units

(c) Negative

(d) None

► (b) Ratios are only valid between quantities of the same kind.

14. 100 ml is what part of 1 litre?

(a) 110

(b) 15

(c) 12

(d) 310

► (a) 100 ml = 110 of 1 litre.

15. Which one is not a ratio?

(a) 2:3

(b) 45

(c) 5 to 6

(d) 3 ÷ 4

► (b) A ratio is written as 4:5, not as a fraction.

16. 2:4 is same as:

(a) 1:2

(b) 4:2

(c) 2:1

(d) 3:2

► (a) 2:4 reduces to 1:2.

17. The ratio of 500 gm to 2 kg is:

(a) 1:2

(b) 1:3

(c) 1:4

(d) 1:5

► (c) 500 g : 2000 g = 1:4.

18. If 3 books cost ₹90, cost of 7 books is:

(a) ₹180

(b) ₹210

(c) ₹250

(d) ₹270

► (b) 1 book = ₹30 ⇒ 7 books = ₹210.