A two number is such that the product of its digits is 6. If 9 is adde

1.	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» ━━━━━━ ◦ ❖ ◦ 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

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»

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

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