Question

In a 3 digit number, sum of the digit is 9 and the unit digit is twice the the the tens digit. on adding 99 to the number, the digit are interchanged. Find the number.​

Answer 1

Answer:

324

Step-by-step explanation:

Let number be in form of xyz.

x + y + z = 9

z is twice of y.

z = 2y

Replacing, z with 2y

x + 3y = 9

Number can be written as :

100x + 10y + z

On adding 99 to number, digit interchange and become zyx.

It can be written as,

100z + 10y + x

Now, writing the equation

100x + 10y + z + 99 = 100z + 10y + x

99x - 99z = -99

x - z = -1

Replacing z with 2y

x - 2y = -1

x + 3y = 9 ( found earlier )

Upon solving, we get

5y = 10

y = 2

So, from above equation we get

x = 3

and

z = 2y

z = 2*2 = 4

So, number is 324.

Thank you.