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