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Question
The product of the digits of a two digit number is 24. If its unit’s digit exceeds twice its ten’s digit by 2; find the number.
Solution
Let the ten’s and unit’s digit of the required number be x and y respectively.
From the given information,
x × y = 24
y = `24/x` ...(1)
Also, y = 2x + 2
`24/x = 2x + 2` ...[Using (1)]
24 = 2x2 + 2x
2x2 + 2x – 24 = 0
x2 + x – 12 = 0
(x + 4)(x – 3) = 0
x = – 4, 3
The digit of a number cannot be negative, so x = 3
∴ y = `24/3` = 8
Thus, the required number is 38.
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