Express each of the following ratios in simplest form:

(i) 75 paise : 3 rupees
(ii) 1 m 5 cm : 63 cm
(iii) 1 hour 5 minutes : 45 minutes
(iv) 8 months : 1 year
(v) (2 kg 250 g) : (3 kg)
(vi) 1 km : 750 m

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Solution

(i) Converting both the quantities into the same unit, we have:
75 paise : (3 $\times$ 100) paise = 75 : 300

= $\frac{75}{300} = \frac{75 \div 75}{300 \div 75} = \frac{1}{4}$ (∵ HCF of 75 and 300 = 75)
= 1 paise : 4 paise

(ii) Converting both the quantities into the same unit, we have:
105 cm : 63 cm = $\frac{105}{63} = \frac{105 \div 21}{63 \div 21} = \frac{5}{3}$ (∵ HCF of 105 and 63 = 21)
= 5 cm : 3 cm

(iii) Converting both the quantities into the same unit
65 min : 45 min = $\frac{65}{45} = \frac{65 \div 5}{45 \div 5} = \frac{13}{9}$ (∵ HCF of 65 and 45 = 5)
= 13 min : 9 min

(iv) Converting both the quantities into the same unit, we get:
8 months : 12 months = $\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$ (∵ HCF of 8 and 12 = 4)
= 2 months : 3 months

(v) Converting both the quantities into the same unit, we get:

2250g : 3000 g = $\frac{2250}{3000} = \frac{2250 \div 750}{3000 \div 750} = \frac{3}{4}$ (∵ HCF of 2250 and 3000 = 750)

= 3 g : 4 g

(vi) Converting both the quantities into the same unit, we get:
1000 m : 750 m = $\frac{1000}{750} = \frac{1000 \div 250}{750 \div 250} = \frac{4}{3}$ (∵ HCF of 1000 and 750 = 250)
= 4 m : 3 m

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Similar questions

Find the ratio of the following in the simplest form:
(i) $75$ paisa to $R s . 3$

(ii) $35$ minutes to $45$ minutes

(iii) $8 k g$ to $400 g m$

(iv) $48$ minutes to $1$ hour

(v) $2$ metres to $35$ cm

(vi) $35$ minutes to $45$ seconds

(vii) $2$ dozen to $3$ scores

(viii) $3$ weeks to $3$ days

(ix) $48$ min to $2$ hour $40$ min

(x) $3 m 5 c m$ to $35 c m$ .

48

60

80

4

45

3

4

45

1 m 5 c m

63 c m

45

4

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