# Q.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 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

(a) 25 cm : 1 m and Rs 40 : Rs 160
1 m = 100 cm
$$\frac{25cm}{100cm} = \frac{1}{4}$$
$$\frac{40}{160} = \frac{1}{4}$$
Yes, these are in a proportion
Middle terms are 1 m, Rs 40 and Extreme terms are 25 cm, Rs 160
(b) 39 litres : 65 litres and 6 bottles : 10 bottles
$$\frac{39}{65} = \frac{3}{5}$$
$$\frac{6}{10} = \frac{3}{5}$$
Yes, these are in a proportion
Middle terms are 65 litres, 6 bottles and Extreme terms are 39 litres, 10 bottles
(c) 2 kg : 80 kg and 25 g : 625 g
$$\frac{2}{80} = \frac{1}{40}$$
$$\frac{25}{625} = \frac{1}{25}$$
No, these are not in a proportion
(d) 200 mL : 2.5 litre and ? 4 : ? 50
2.5 litre = 2500 ml
$$\frac{200}{2500} = \frac{2}{25}$$
$$\frac{4}{50} = \frac{2}{25}$$
Yes, these are in a proportion
Middle terms are 2.5 litres, Rs 4 and Extreme terms are 200 ml, Rs 50