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 ml and ₹4 : ₹50

(a) 25 cm : 1 m = 25 cm : (1 x 100) cm = 25 cm : 100 cm = 25/100 = 1/4 = 1 : 4
₹40 : ₹160 = 40/160 = 1/4 = 1 : 4
Since the ratios are equal, therefore these are in proportion.
Middle terms = 1 m, ₹40 and Extreme terms = 25 cm, ₹160

(b) 39 litres : 65 litres = 39/65=3/5
6 bottles : 10 bottles = 6/10 = 3/5 = 3:5
Since the ratios are equal, therefore these are in proportion.
Middle terms = 65 litres, 6 bottles and Extreme terms = 39 litres, 10 bottles

(c) 2 kg : 80 kg = 2/80=1/40= 1 : 40
25 g : 625 g = 25/625=1/25=1:25
Since the ratios are not equal, therefore these are not in proportion.

(d) 200 ml :2.5 litres =200 ml:(25000)litres=200 ml : 2500 ml=200/2500=2/25=2:25
₹4:₹50= 4/50=2/25=2:25
Since the ratios are equal, therefore these are in proportion.
Middle terms = 2.5 litres, ₹4 and Extreme terms = 200 ml, ₹50

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