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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

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Solution

## (1) 25 beads : 40 beads = $\frac{25}{40}=\frac{25÷5}{40÷5}=\frac{5}{8}$ = 5 : 8 (HCF of 25 and 40 = 5) (2) 40 rupees : 120 rupees = $\frac{40}{120}=\frac{40÷40}{120÷40}=\frac{1}{3}$ = 1 : 3 (HCF of 40 and 120 = 40) (3) 15 minutes : 1 hour = 15 minutes : 60 minutes = $\frac{15}{60}=\frac{15÷15}{60÷15}=\frac{1}{4}$ = 1 : 4 (HCF of 15 and 60 = 4) (4) 30 litres : 24 litres = $\frac{30}{24}=\frac{30÷6}{24÷6}=\frac{5}{4}$ = 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 = $\frac{99}{44}=\frac{99÷11}{44÷11}=\frac{9}{4}$ = 9 : 4 (HCF of 99 and 44 = 11) (6) 1 L : 250 mL = 1000 mL : 250 mL = $\frac{1000}{250}=\frac{1000÷250}{250÷250}=\frac{4}{1}$ = 4 : 1 (HCF of 1000 and 250 = 250) (7) 60 paise : 1 rupee = 60 paise : 100 paise = $\frac{60}{100}=\frac{60÷20}{100÷20}=\frac{3}{5}$ = 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 = $\frac{750}{500}=\frac{750÷250}{500÷250}=\frac{3}{2}$ = 3 : 2 (HCF of 750 and 500 = 250) (9) 125 cm : 1 metre = 125 cm : 100 cm = $\frac{125}{100}=\frac{125÷25}{100÷25}=\frac{5}{4}$ = 5 : 4 (HCF of 125 and 100 = 25)

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