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Question
A two digit number contains the bigger at ten’s place. The product of the digits is 27 and the difference between two digits is 6. Find the number.
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Solution
Let unit’s digit = x
then tens digit = x + 6
Number = x + 10(x + 6)
= x + 10x + 60
= 11x + 60
According to the condition,
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
Either x + 9 = 0,
then x = -9,
but it is not possible as it is negative.
or
x - 3 = 0,
then x = 3
∴ Number
= 11x + 60
= 11 × 3 + 60
= 33 + 60
= 93
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