Question

If A:B= 3:4 and B:C= 6:7, find:(1) A:B:C (2) A:C

Answer 1

(1) A: B: C (2) A: C is C ) 9:12:14 , 9:14

Step-by-step explanation:

We know that

$\frac{a}{b}=\frac{3}{4} \rightarrow(i)$

$\frac{b}{c}=\frac{6}{7} \rightarrow(i i)$

Taking LCM in both the cases of b,  

4 and 6 are the two numbers of b.

$4=2 \times 2$

$6=2 \times 3$

The LCM of b is $2 \times 2 \times 3=12$

Then equalise b by multiplying 3 in (i)

$\frac{a}{b}=\frac{9}{12}$

Then equalise b by multiplying 2 in (ii)

$\frac{b}{c}=\frac{12}{14}$

Then, form a, b, c in the ratio form.

That is $a:b:c = 9:12:14$

Therefore,  

The value of a is 9

The value of b is 12

The value of c is 14

By substituting the values of a and b,

Then a : b becomes, 9 : 14

$a : b=9 : 14$

Answer 2

Answer:

9:14

Step-by-step explanation:

(1) A: B: C (2) A: C is C ) 9:12:14 , 9:14

Step-by-step explanation:

We know that

\frac{a}{b}=\frac{3}{4} \rightarrow(i)ba=43→(i)

\frac{b}{c}=\frac{6}{7} \rightarrow(i i)cb=76→(ii)

Taking LCM in both the cases of b,  

4 and 6 are the two numbers of b.

4=2 \times 24=2×2

6=2 \times 36=2×3

The LCM of b is 2 \times 2 \times 3=122×2×3=12

Then equalise b by multiplying 3 in (i)

\frac{a}{b}=\frac{9}{12}ba=129

Then equalise b by multiplying 2 in (ii)

\frac{b}{c}=\frac{12}{14}cb=1412

Then, form a, b, c in the ratio form.

That is a:b:c = 9:12:14a:b:c=9:12:14

Therefore,  

The value of a is 9

The value of b is 12

The value of c is 14

By substituting the values of a and b,

Then a : b becomes, 9 : 14

a : b=9 : 14

a:b=9:14