Ratio and Proportion - 2. If a:b=2:3,b:c=4:5 then find a:b:c Examples

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Ratio and Proportion - 2. If `a:b=2:3,b:c=4:5` then find `a:b:c` example ( Enter your problem )

( Enter your problem )

Examples

Other related methods

1. If `a:b:c=2:3:5` then find value of `(a^2+b^2+c^2)/(ab+bc+ca)`
(Previous method)

3. If `a/b=c/d=e/f` then prove that `(2a+3c-4e)/(2b+3d-4f)=(5a-4c+3e)/(5b-4d+3f)`
(Next method)

1. Examples

1. If `a:b=2:3,b:c=4:5` then find `a:b:c`

Solution:
`a:b=2:3,b:c=4:5`

Here, `a:b=2:3` and `b:c=4:5`

In the given ratios `b` is the common term, and the values of `b` in both ratios are `3` and `4`, which are not equal. To make them equal, find the L.C.M. of `3` and `4`.

L.C.M. of `3` and `4 = 12`

Multiplity `1^(st)` ratio by `4`

`a:b=2:3=2 xx 4:3 xx 4=8:12`

Multiplity `2^(nd)` ratio by `3`

`b:c=4:5=4 xx 3:5 xx 3=12:15`

`:.a:b:c=8:12:15`

2. If `2a=3b=7c` then find `a:b:c`

Solution:
`2a=3b=7c`

Let `2a=3b=7c=k` (say)

`:. 2a=k,3b=k,7c=k`

`:.a=k/2,b=k/3,c=k/7`

`:.a:b:c=k/2:k/3:k/7=42 xx k/2:42 xx k/3:42 xx k/7=21:14:6`

(L.C.M. of `2,3,7 = 42`)

This material is intended as a summary. Use your textbook for detail explanation.
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