the value of x in the proportion ,8:6::24:(x-4)
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Answer:
Page No 124:
Question 1:
Express each of the following ratios in simplest form:
(i) 24 : 40
(ii) 13.5 : 15
(iii) 6
2
3
:7
1
2
(iv)
1
6
:
1
9
(v) 4:5:
9
2
(vi) 2.5 : 6.5 : 8
ANSWER:
(i) HCF of 24 and 40 is 8.
∴ 24 : 40 =
24
40
=
24 ÷ 8
40 ÷ 8
=
3
5
= 3 : 5
Hence, 24 : 40 in its simplest form is 3 : 5.
(ii) HCF of 13.5 and 15 is 1.5.
13.5
15
=
135
150
The HCF of 135 and 150 is 15.=
135 ÷ 15
150 ÷ 15
=
9
10
Hence, 13.5 : 15 in its simplest form is 9 : 10.
(iii)
20
3
:
15
2
=40 : 45
The HCF of 40 and 45 is 5.
∴ 40 : 45 =
40
45
=
40 ÷ 5
45 ÷ 5
=
8
9
= 8 : 9
Hence, 6
2
3
: 7
1
2
in its simplest form is 8 : 9
(iv) 9 : 6
The HCF of 9 and 6 is 3.
∴ 9 : 6 =
9
6
=
9 ÷ 3
6 ÷ 3
= 3 : 2
Hence,
1
6
:
1
9
in its simplest form is 3 : 2.
(v) LCM of the denominators is 2.
∴ 4 : 5 :
9
2
= 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 =
25
65
80
=
25 ÷ 5
65 ÷ 5
80 ÷ 5
=
5
13
16
= 5 : 13 : 16
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