Question

Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios from a proportion. 

(i) 200 cm : 2.5 m and Rs. 40 : Rs. 5 

(ii) 1 kg : 250 gm and Rs. 40 : Rs. 10 

(iii) 4 kg : 16 gm and 20 gm : 400 gm 

(iv) 39 Persons : 65 Persons and 9l : 15l

Answer 1

(i) 200 cm : 2.5 gm and Rs. 40 : Rs. 5 

⇒ 2 : 2.5 :: 40 : 5 (∵ 200 cm = 2 m) 

⇒ 2 × 5 = 2.5 × 40

 ⇒ 10 = 100 

∴ This statement is not in a proportion. 

(ii) 1 kg : 250 gm and 40 Rupees : 10 Rupees 

1 kg = 1000 gm 

⇒ 1000 gm : 250 gm :: 40 Rupees : 10 Rupees 

1 kg = 1000 gm 

⇒ 1000 : 250 :: 40 : 10 

⇒ 1000 × 10 = 250 × 40 

⇒ 10000 = 10000 

This statement makes a proportion its middle terms are 250 gm and Rs. 40 Rupees, and extreme terms are 1 kg and Rs. 10 

(iii) 4 kg : 16 kg and 20 gm : 400 gm 

⇒ 4 : 16 20 : 400 

⇒ 4 × 400 = 16 × 20

⇒ 1600 = 320 

This statement is not in a proportion 

(iv) 39 Person : 65 Person and 9l : 15l 

⇒ 39 : 65 :: 9 : 15 

⇒ 39 × 15 = 65 × 9 

⇒ 585 = 585 

This statement makes a proportion. Its middle terms are 65 persons and 9l. and extreme terms are 39 persons and 15l.