Question

The sum of digits of a two digit number is 9 the digit is reversed the new number decreased by 9 is equal to 4 times of orginal number find orginal number

Answer 1

Answer:

$\boxed{\boxed{The \;required \;number\; is\; 18.}}$

Step-by-step explanation:

Let the digit in the ten's place be  x.

Let the digit in the unit place be y.

∴ The number will be = 10x+y

Also the sum of digits = 9

$\implies$ x+y = 9 $\longrightarrow$ (1)

On Reversing the order,the number we get will be

10y+x

Now From the question,

(10y+x−9) = 4(10x+y)

On simplification,

10y+x-9= 40x+4y

-9 = 40x + 4y - 10y - x

-9 = 39x - 6y

39x - 6y +9 = 0

We can take 3 as common in the above equation , so on dividing by 3,

13x - 2y + 3 = 0 $\longrightarrow$ (2)

From equation (1) we can derive the value of x ,

x = 9 - y $\longrightarrow$ (3)

On substituting value of x in (2) we get,

13 (9−y) −2y + 3 = 0

117 - 13y -2y +3 =0

117 - 15y + 3 = 0

120 - 15y = 0

120 = 15y

y = 120/15 = 8

On substituting value of y in (3),

x = 9 - 8

x = 1

∴ The required number = 18