Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
(a) 25 cm : 1 m and ₹ 40 : ₹ 160
(b) 39 litres : 65 litres and 6 bottles : 10 bottles
(c) 2 kg : 80 kg and 25 g : 625 g
(d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50

Solution:

We will use the concept of proportion to solve this.

(a) 25 cm : 1 m and ₹ 40 : ₹ 160

⇒ 25 cm = 25 / 100 m = 0.25 m

⇒ 0.25 / 1 = 1 / 4

⇒ 40 / 160 = 1 / 4

⇒ 1 / 4 = 1 / 4

Therefore, 25 cm : 1 m and ₹ 40 : ₹ 160 are in proportion.

Middle terms = 1 m, ₹ 40 and Extreme terms = 25 cm, ₹ 160

(b) 39 litres : 65 litres and 6 bottles : 10 bottles

⇒ 39 / 65 = 3 / 5

⇒ 6 / 10 = 3 / 5

⇒ 3 / 5 = 3 / 5

Therefore, 39 liters: 65 liters and 6 bottles: 10 bottles are in proportion.

Middle terms = 65 liters, 6 bottles and Extreme terms = 39 liters, 10 bottles

(c) 2 kg : 80 kg and 25 g : 625 g

⇒ 2 / 80 = 1 / 40

⇒ 25 / 625 = 1 / 25

⇒ 1 / 40 ≠ 1 / 25

Therefore, 2 kg: 80 kg and 25 g: 625 g are not in proportion.

(d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50

⇒ 2.5 litre = 2500 ml

⇒ 200 / 2500 = 2 / 25

⇒ 4 / 50 = 2 / 25

⇒ 2 / 25 = 2 / 25

Therefore, 200 mL: 2.5 liters and ₹ 4: ₹ 50 are in proportion.

Middle terms = 2.5 liters, ₹ 4 and Extreme terms = 200 ml, ₹ 50

You can also use Proportions Calculator to check your answer.

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NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.2 Question 4

Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion. (a) 25 cm : 1 m and ₹ 40 : ₹ 160 (b)39 litres : 65 litres and 6 bottles : 10 bottles (c) 2 kg : 80 kg and 25 g : 625 g (d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50

Summary:

1. Yes, 25 cm : 1 m and ₹ 40 : ₹ 160 are in proportion. Middle terms = 1 m, ₹ 40 and Extreme terms = 25 cm, ₹ 160
2. Yes, 39 litres : 65 litres and 6 bottles : 10 bottles are in proportion. Middle terms = 65 liters, 6 bottles and Extreme terms = 39 liters, 10 bottles
3. No, 2 kg : 80 kg and 25 g : 625 g are not in proportion
4. Yes, 200 mL : 2.5 litre and ₹ 4 : ₹ 50 are in proportion. Middle terms = 2.5 liters, ₹ 4 and Extreme terms = 200 ml, ₹ 50

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