Question

A two number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places.Find the number.​

Answer 1

━━━━━━ ◦ ❖ ◦  ANSWER  ━━━━━━ ◦ ❖ ◦

Let us assume  the two digit number to be ,  x + 10 y

It is also given that the product of its digits is 6 , $\implies$ x × y = 6$\longrightarrow$ (1)

It is also told that if  9 is added to the number, the digits interchange their places ,  $\implies$ 10x + y + 9 = 10y + x  $\longrightarrow$ (2)

On Solving (2) ,

10x + y  + 9 = 10y + x

( 10x - x ) + ( y - 10 y ) +9 = 0

9x - 9y + 9 = 0

x − y + 1 = 0

y = x + 1  $\longrightarrow$ (3)

Substituting the value of y in (3) in (1)

x ( x + 1 ) = 6

x² + x = 6

Now Let us Solve the equation , x² + x = 6

x² + x - 6

Product = -6

Sum = +1

$\implies$ x² + 3x − 2x −6 = 0

$\implies$ (x+3) (x−2) = 0

x = -3

and

x = 2

Therefore x = 2 , substituting x = 2 in x + 10 y we get ,

∴ The  two digit number = 10×2 + 3 = 23

Let us Verify The Answer :-

23 + 9 = 32 , Here the digit got reversed so our answer is correct