Question

A certain number between 10 and100 is 4 timea the sum of its digits and if 18 is added to it, tha digits will be reversed.Find the number.

Answer 1

Let the 1st digit be x and the 2nd digit be y.

Thus the no. is 10x + y.

Now, atq: 10x + y= 4(x+y)
=> 6x=3y
=> 2x=y
=> 2x - y = 0 --------1.

and 10x + y + 18= 10y + x
=> 9x -9y + 18 = 0
=> x - y + 2 = 0 --------2.

Solving 1. and 2.,
2x - y = 0
2x - 2y + 4 = 0
---------------------------
y - 4 = 0
=> y=4 --------- 3.

Putting 3. in 1.,
2x - 4 = 0
=> x = 2

Thus, the no. is 10x + y = 24.