Question

If A:B = 2:3 and B:C = 6:7 then find A:B:C​

Answer 1

Answer:

• a : b : c = 8 : 12 : 14

Given :

• A : B = 2 : 3

• B : C = 6 : 7

To find :

• Value of, A:B:C =?

Step-by-step explanation:

We know that

a/b = 2/3 ..... (i)

b/c = 6/7 ..... (ii)

Taking LCM in both the cases of b,

3 and 6 are the two numbers of b.

3 = 1 x 3

6 = 3 x 2

The LCM of b is = 3 x 3 x 2 = 18

Then equalise b by multiplying 4 in (i)

a/b = (2/3) x 4

a/b = 8/12

Then equalise (b) by multiplying 2 in (ii)

b/c = (6/7) x 2

b/c = 12/14

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

That is a:b:c = 8 : 12 : 14

Therefore,

• The value of a is 8.

• The value of b is 12.

• The value of c is 14.

Answer 2

$\huge {\red {\mathfrak {Question:}}}$

• If A:B=2:3 and B:C=6:7, then find A:B:C.

$\huge {\red {\mathfrak {Solution:}}}$

$\underline {\bold {Given:}}$

• A:B= 2:3
• B:C=6:7

$\underline {\bold {To\:find:}}$

• A:B:C

To find A:B:C we have to make value of b equal in both(in A:B andB:C).

$\rule {191}{2}$

$\implies A : B = 2 : 3\\\\ \implies \frac{A}{B} = \frac{2}{3}$

$\rule {87}{1}$

$\implies B:C= 6 : 7\\\\ \implies \frac{B}{C} = \frac{6}{7}$

$\rule {191}{2}$

$\implies A : B = 2 : 3\\\\ \implies \frac{A}{B} = \frac{2}{3} \\\\ \implies \frac{A}{B} = \frac{2 \times 2}{3 \times 2} \\\\ \implies \frac{A}{B} = \frac{4}{6}$

$\rule {87}{1}$

$\implies B:C= 2 : 3\\\\ \implies \frac{B}{C} = \frac{6}{7} \\\\ \implies \frac{B}{C} = \frac{6\times 1}{7\times 1} \\\\ \implies \frac{B}{C} = \frac{6}{7}$

$\rule {191}{2}$

$\green {\therefore{A:B:C=4:6:7}}$