Question

Find the reduced form of the ratio of the first quantity to second quantity.

(i) 700 rs, 308 rs (ii) 14 rs, 12 rs. 40 paise. (iii) 5 litre, 2500 ml (iv) 3 years 4 months, 5years 8 months (v) 3.8 kg, 1900 gm

(vi) 7 minutes 20 seconds, 5 minutes 6 seconds.

Answer 1

(i)
Rs 700 : Rs 308 = $\frac{700}{308}=\frac{{\displaystyle 700÷28}}{{\displaystyle 308÷28}}=\frac{25}{11}$ = 25 : 11 (HCF of 700 and 308 = 28)

(ii)
14 rupees = 1400 p

12 rupees 40 paise = 1200 + 40 = 1240 p

∴ 14 rupees : 12 rupees 40 paise = 1400 p : 1240 p = $\frac{1400}{1240}=\frac{{\displaystyle 1400÷40}}{{\displaystyle 1240÷40}}=\frac{35}{31}$ = 35 : 31 (HCF of 1400 and 1240 = 40)

(iii)
5 litre = 5000 mL (1 L = 1000 mL)

∴ 5 litre : 2500 mL = 5000 mL : 2500 mL = $\frac{5000}{2500}=\frac{5000÷2500}{2500÷2500}=\frac{2}{1}$ = 2 : 1 (HCF of 5000 and 2500 = 2500)

(iv)
3 years 4 months = 3 years + 4 months = 3 × 12 + 4 = 36 + 4 = 40 months (1 year = 12 months)

5 years 8 months = 5 years + 8 months = 5 × 12 + 8 = 60 + 8 = 68 months

∴ 3 years 4 months : 5 years 8 months = 40 months : 68 months = $\frac{40}{68}=\frac{{\displaystyle 40÷4}}{{\displaystyle 68÷4}}=\frac{10}{17}$ = 10 : 17 (HCF of 40 and 68 = 4)

(v)
3.8 kg = 3.8 × 1000 = 3800 g (1 kg = 1000 g)

∴ 3.8 kg : 1900 g = 3800 g : 1900 g = $\frac{3800}{1900}=\frac{3800÷1900}{1900÷1900}=\frac{2}{1}$ = 2 : 1 (HCF of 3800 and 1900 = 1900)

(iv)
7 minutes 20 seconds = 7 minutes + 20 seconds = 7 × 60 + 20 = 420 + 20 = 440 seconds (1 minute = 60 seconds)

5 minutes 6 seconds = 5 minutes + 6 seconds = 5 × 60 + 6 = 300 + 6 = 306 seconds

∴ 7 minutes 20 seconds : 5 minutes 6 seconds = 440 seconds : 306 seconds = $\frac{440}{306}=\frac{440÷2}{306÷2}=\frac{220}{153}$ = 220 : 153 (HCF of 220 and 153 = 2)