1. If `a/b=2/3` then find value of `(2a-3b)/(a-2b)`

Solution:
`a/b=2/3`

`:.a/2=b/3`

Let `a/2=b/3=k` (say)

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

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

Now `(2a-3b)/(a-2b)`

`=(4k-9k)/(2k-6k)`

`=(-5k)/(-4k)`

Cancel the common factor `-k`

`=(5)/(4)`

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

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

Let `a:2=b:3=c:5=k` (say)

`:. a:2=k,b:3=k,c:5=k`

`:.a=2k,b=3k,c=5k`

Now `(a^2+b^2+c^2)/(ab+bc+ca)`

`=(4k^2+9k^2+25k^2)/(6k^2+15k^2+10k^2)`

`=(38k^(2))/(31k^(2))`

Cancel the common factor `k^(2)`

`=(38)/(31)`

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