Question

2.07.
If a : b = b:c= 2:3, find a : bic

Answer 1

Answer:

A:B = 2:3 & B:C=7:8 , then A:B:C ?

Since B is common in both , we have to reach a common number for B in both ratios A:B & B:C , so that in proportion to that common number we can get the value of A & C too.

Since, B has no common factor ,so common number will be a achieved by a simple multiplication of 3*7 which is equal to 21.

Actually, 21 is L.C.M. of 3 & 7.

Now,

When B is 21 , A will be 14 (A= 21*2/3)

When B is 21, C will be 24 (C= 21*8/7)

Hence, A:B:C = 14:21:24

Answer 2

THE QUESTION WILL BE a:b:c

Given,

$\frac{a}{b} = \frac{b}{c} = \frac{2}{3}$

this means,

$a = \frac{2}{3} b$

$c = \frac{3}{2} b$

a:b:c

=>

$\frac{2}{3} b:b: \frac{3}{2} b$

$= \frac{2}{3} :1: \frac{3}{2}$

$= \frac{2}{3} \times 6:1 \times 6: \frac{3}{2} \times 6$

= 4 : 6 : 9

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