1)Find the ratio of each of the following in simplest form:
(i) Rs 7.80 to 65 paise (ii) 15 hours to 1 day
(iii) 750 gm to 2 kg (iv) 64 ml to 1 litre
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Answers
Step-by-step explanation:
Express each of the following ratios in simplest form:
(i) 24 : 40
(ii) 13.5 : 15
(iii) 623:712
(iv) 16:19
(v) 4:5:92
(vi) 2.5 : 6.5 : 8
ANSWER:
(i) HCF of 24 and 40 is 8.
∴ 24 : 40 = 2440= 24 ÷ 840 ÷ 8= 35 = 3 : 5
Hence, 24 : 40 in its simplest form is 3 : 5.
(ii) HCF of 13.5 and 15 is 1.5.
13.515=135150The HCF of 135 and 150 is 15.=135 ÷ 15150 ÷ 15=910
Hence, 13.5 : 15 in its simplest form is 9 : 10.
(iii) 203 : 152=40 : 45
The HCF of 40 and 45 is 5.
∴ 40 : 45 = 4045=40 ÷ 545 ÷ 5=89 = 8 : 9
Hence, 623 : 712 in its simplest form is 8 : 9
(iv) 9 : 6
The HCF of 9 and 6 is 3.
∴ 9 : 6 = 96=9 ÷ 36 ÷ 3 = 3 : 2
Hence, 16:19 in its simplest form is 3 : 2.
(v) LCM of the denominators is 2.
∴ 4 : 5 : 92 = 8 : 10 : 9
The HCF of these 3 numbers is 1.
∴ 8 : 10 : 9 is the simplest form.
(vi) 2.5 : 6.5 : 8 = 25 : 65 : 80
The HCF of 25, 65 and 80 is 5.
∴ 25 : 65 : 80 = 256580= 25 ÷ 565 ÷ 580 ÷ 5=51316 = 5 : 13 : 16
Page No 124:
Question 2:
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
ANSWER:
(i) Converting both the quantities into the same unit, we have:
75 paise : (3 × 100) paise = 75 : 300
= 75300= 75 ÷ 75300 ÷ 75=14 (∵ 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 = 10563=105÷2163÷21= 53 (∵ HCF of 105 and 63 = 21)
= 5 cm : 3 cm
(iii) Converting both the quantities into the same unit
65 min : 45 min = 6545= 65÷545÷5=139 (∵ 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 = 812=8÷412÷4=23 (∵ HCF of 8 and 12 = 4)
= 2 months : 3 months
(v) Converting both the quantities into the same unit, we get:
2250g : 3000 g = 22503000=2250÷7503000÷750= 34 (∵ 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 = 1000750=1000÷250750÷250 = 43 (∵ HCF of 1000 and 750 = 250)
= 4 m : 3 m
Page No 124:
Question 3:
If A : B = 7 : 5 and B : C = 9 : 14, find A : C.
ANSWER:
AB = 75 and BC = 914
Therefore, we have:
AB×BC = 75×914AC = 910
∴ A : C = 9 : 10
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Step-by-step explanation:
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