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Two numbers are in the ratio 5 : 6. If 8...

Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5, then find the numbers.

Text Solution

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Let the numbers be 5x and 6x respectively. So, new numbers after subtracting 8 from each will be (5x - 8) and (6x - 8) respectively.
Now, the ratio of new numbers is `4 : 5`.
`therefore" " (5x - 8)/(6x - 8) = (4)/(5)`
implies 25x - 40 = 24x - 32
implies 25x - 24x = 40 - 32
implies x = 8
`therefore` Required numbers = 5x and 6x become `5xx8, 6xx8`
i.e., Required numbers = 40 and 48.
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