Question

a number consists of two digits whose sum is 8. If 18 is added to the number, its digits are reversed. find the number.

a. 38 b. 35 c.53

Answer 1

Let the numbers be 10x and y
So,10x+y=8-----------------1
then, 10y+x-------------------2
From 1 and 2 we derive !!
10x+y+18=10y+x
             9y=9x+18
 9x-9y+18=0--------------3
y=x+2----------------------4
substituting 4 in 1

Henceforth,
the no will be 35

Answer 2

sum of two digits is 8 so take digit as A and B
so, A + B = 8........[1]
and for original no. 10A + B.....[2]
add 18 in this so, 10A + B + 18 
the num. is reversed so 10B + A
10A + B + 18 = 10B + A
9A - 9B = -18
A - B = -2......[3]
from 3 A = -2 +B
put this in 1 and 
-2 + B + B = 8
so B = 5
and form that A = 3
so no is 10[3] + 5 = 35 form eq. 2 
the no is 35 
but after adding 18 => 35 + 18 = 53