Question

Find the ratio of the first quantity to the second.
(1) 25 beads, 40 beads (2) 40 rupees, 120 rupees (3) 15 minutes, 1 hour
(4) 30 litres, 24 litres (5) 99 kg, 44000 grams (6) 1 litre, 250 ml
(7) 60 paise, 1 rupee (8) 750 grams, $\frac{1}{2}$kg (9) 125 cm, 1 metre

Answer 1

(1) 25 beads : 40 beads = $\frac{25}{40}=\frac{{\displaystyle 25÷5}}{{\displaystyle 40÷5}}=\frac{5}{8}$ = 5 : 8 (HCF of 25 and 40 = 5)

(2) 40 rupees : 120 rupees = $\frac{40}{120}=\frac{{\displaystyle 40÷40}}{{\displaystyle 120÷40}}=\frac{1}{3}$ = 1 : 3 (HCF of 40 and 120 = 40)

(3) 15 minutes : 1 hour = 15 minutes : 60 minutes = $\frac{15}{60}=\frac{{\displaystyle 15÷15}}{{\displaystyle 60÷15}}=\frac{1}{4}$ = 1 : 4 (HCF of 15 and 60 = 4)

(4) 30 litres : 24 litres = $\frac{30}{24}=\frac{{\displaystyle 30÷6}}{{\displaystyle 24÷6}}=\frac{5}{4}$ = 5 : 4 (HCF of 30 and 24 = 6)

(5) 44000 g = $\frac{44000}{1000}$ = 44 kg (1 kg = 1000 g)

∴ 99 kg : 44000 g = 99 kg : 44 kg = $\frac{99}{44}=\frac{{\displaystyle 99÷11}}{{\displaystyle 44÷11}}=\frac{9}{4}$ = 9 : 4 (HCF of 99 and 44 = 11)

(6) 1 L : 250 mL = 1000 mL : 250 mL = $\frac{1000}{250}=\frac{{\displaystyle 1000÷250}}{{\displaystyle 250÷250}}=\frac{4}{1}$ = 4 : 1 (HCF of 1000 and 250 = 250)

(7) 60 paise : 1 rupee = 60 paise : 100 paise = $\frac{60}{100}=\frac{{\displaystyle 60÷20}}{{\displaystyle 100÷20}}=\frac{3}{5}$ = 3 : 5 (HCF of 60 and 100 = 20)

(8) $\frac{1}{2}$ kg = $\frac{1}{2}$ × 1000 g = 500 g (1 kg = 1000 g)

∴ 750 g : $\frac{1}{2}$ kg = 750 g : 500 g = $\frac{750}{500}=\frac{{\displaystyle 750÷250}}{{\displaystyle 500÷250}}=\frac{3}{2}$ = 3 : 2 (HCF of 750 and 500 = 250)

(9) 125 cm : 1 metre = 125 cm : 100 cm = $\frac{125}{100}=\frac{{\displaystyle 125÷25}}{{\displaystyle 100÷25}}=\frac{5}{4}$ = 5 : 4 (HCF of 125 and 100 = 25)