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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.
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 x 3 + 60
= 33 + 60
= 93.
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