Question

Given that a : b:c = 75: 120 : 132
(i) simplify a : b:c,
ii) find b:a,
iii) find b:c.​

Answer 1

$\sf { \underline{SOLUTION}}$

GIVEN

a : b : c = 75 : 120 : 132

TO DETERMINE

(i) To simplify a : b : c

ii) To find b : a

iii) To find b : c

EVALUATION

Here it is given that

a : b : c = 75 : 120 : 132

(i) Here

75 = 3 × 5 × 5

120 = 2 × 2 × 2 × 3 × 5

132 = 2 × 2 × 3 × 11

So the HCF of 75, 120, 132 = 3

Dividing each term of the ratio by 3 we get

a : b : c = 25 : 40 : 44

Which is required simplest form

ii) From above

a : b = 25 : 40

∴ b : a = 40 : 25

iii) Again from above

b : c = 40 : 44

40 = 2 × 2 × 2 × 5

44 = 2 × 2 × 11

HCF of 24 & 44 = 4

Divide each term by 4

∴ b : c = 10 : 11

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Answer 2

Answer:

a:b:c = 25:40:44 (simplified)

b:a = 8:5 (simplified)

b:c = 10:11 (simplified)

Step-by-step explanation:

a:b:c ---> 75:120:132

SIMPLIFYING a:b:c :

First, find out the HCF of 75, 120 and 132.

120 and 75 :

120 = 75*1 + 45

=> 75 = 45*1 + 30

=> 45 = 30*1 + 15

=> 30 = 15*2 + 0

Now, 15 and 132 :

132 = 15*8 + 12

=> 15 = 12*1 + 3

=> 12 = 3*4 + 0

Thus, HCF of 75, 120 and 132 is 3.

Now divide all three nos. by 3.

75/3: 120/3: 132/3

=> 25:40:44 is the simplified form of 75:120:132.

FINDING b:a :

As a:b:c = 25:40:44,

b:a = 40:25 => 8:5       (Dividing by 5)

FINDING b:c :

As a:b:c = 25:40:44,

b:c = 40:44 => 10:11       (Dividing by 4)