Three numbers are in the ratio of $4 : 5 : 6$ . If the sum of the largest and smallest equals the sum of the third and $55$ , find the numbers.

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Solution

Let the numbers be $4 x, 5 x$ and $6 x$ .
$6 x + 4 x = 5 x + 55$
$10 x - 5 x = 55$
$5 x = 55$
$x = 55 / 5 = 11$
Hence, the numbers are $44, 55$ and $66$ .

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