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`