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.

Answer 1

Let the bigger number be 'a'.

$\to$the smaller number is 'a-6'

Place value	Face value	Place value	Face value
10	a	1	a-6

In expanded form the number becomes $[10\times a]+[1\times (a-6\left)\right]$

$\to$ 10a + a - 6 = 11a - 6

ATQ:-

$\to$a x (a-6) = 27

$\to a^2-6a=27$

$\to a^2-6a-27=0.$

$\to (a-9)(a+3)=0$

$\to a=9ora=-3$

CASE - I :

When a = -3,

the two digit number = 11a - 6 = -33 -6 = -39

This isn't the possible two digit number required as the bigger number should be at ten's place.

CASE - II :

When a = 9,

the two digit number = 11a - 6 = 99 -6 = 93

Therefore, this is the possible two digit number required as the bigger number is at ten's place.

Therefore, the 2-digit number is 93.