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


Answer :

(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

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