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Question
In a two-digit number, the ten’s digit is bigger. The product of the digits is 27 and the difference between two digits is 6. Find the number.
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Solution
Given, the difference between the two digits is 6 and the ten’s digit is bigger than the unit’s digit.
So, let the unit’s digit be x and ten’s digit be (x + 6).
From the given condition, we have:
x(x + 6) = 27
x2 + 6x – 27 = 0
x2 + 9x – 3x – 27 = 0
x(x + 9) – 3(x + 9) = 0
(x + 9)(x – 3) = 0
x = –9, 3
Since, the digits of a number cannot be negative.
So, x = 3.
Unit’s digit = 3
Ten’s digit = 9
Thus, the number is 93.
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