Question

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 Rs 40 : Rs 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  Rs 4 : Rs 50

Answer 1

(a) 25 cm : 1m and Rs 40: Rs160

= 25 cm : 1m

= 25 cm : (1 x 100) cm

= 25 cm : 100 cm = \(\frac{25}{100}\)

= \(\frac{1}{4}\) = 1:4

Rs. 40 : Rs. 160 = \(\frac{40}{160}\)

= \(\frac{1}{4}\) = 1:4

Since the ratios are equal, therefore these are in proportion.
Middle terms = 1 m, Rs 40 and Extreme terms = 25 cm, Rs160 
(b) 39 litres : 65 litres and 6 bottles : 10 bottles

= 39 liters : 65 liters

= \(\frac{39}{65}\)

= \(\frac{3}{5}\)
= 6 bottles : 10 bottles

=\(\frac{6}{10}\)

= \(\frac{3}{5}\)

= 3:5

Since the ratios are equal, therefore these 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 kg : 80 kg

= \(\frac{2}{80}\)

= \(\frac{1}{40}\)

= 1:40

= 25 g : 625 g

= \(\frac{25}{625}\)

= \(\frac{1}{25}\)

= 1:25

Since the ratios are not equal, therefore these are not in proportion. 

(d) 200 mL : 2.5 litre and Rs 4 : Rs 50

= 200 ml : 2.5 liters

= 200 ml : (25 x 1000) liters

= 200 ml : 2500 ml

= \(\frac{200}{2500}\)

= \(\frac{2}{25}\)

= 2:25

= Rs 4 : Rs 50 = \(\frac{4}{50}\)

= \(\frac{2}{25}\)

= 2:25

Since the ratios are equal, therefore these are in proportion.
Middle terms = 2.5 liters, Rs. 4 and Extreme terms = 200 ml, Rs. 50