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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