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.

Answer 1

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