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Question
Arrange 5: 6, 8: 9, 13: 18 and 7: 12 in ascending order of magnitude.
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Solution
The given ratios are 5: 6, 8: 9, 13: 18 and 7: 12.
Now L.C.M., of 6, 9, 18 and 12 = 36
Now `(5)/(6) = (5 xx 6)/(6 xx 6) = (30)/(36)`
`(8)/(9) = (8 xx 4)/(9 xx 4) = (32)/(36)`
`(13)/(18) = (13 xx 2)/(18 xx 2) = (26)/(36)`
Also `(7)/(12) = (7 xx 3)/(12 xx 3) = (21)/(36)`
Here `(21)/(36) < (26)/(36) < (30)/(36) < (32)/(36)`
Hence `(7)/(12) < (13)/(18) < (5)/(6) < (8)/(9)`
i.e., Ascending order
7 : 12 < 13 : 18 < 5 : 6 < 8 : 9.
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