Question

If [ab] [2/3] =[14] [a/b]. Prove that [a=b]​

Answer 1

Answer:

A:B:C=2:3:4

Let the numbers be A=2x,B=3x,C=4x such that the ratio is maintained.

∴

B

A

=

3x

2x

,

C

B

=

4x

3x

,

A

C

=

2x

4x

⇒

B

A

=

3

2

,

C

B

=

4

3

,

A

C

=2

We multiply the ratios by 12.

12 was chosen because this will ensure that the ratio of

B

A

,

C

B

and

A

C

comes out to be a whole number.

Hence,

B

A

=

3

2

×12=8

C

B

=

4

3

×12=9

A

C

=2×12=24

∴

B

A

:

C

B

:

A

C

=8:9:24