Question

The digits of a two-digit number differ by 3. If the digits are interchanged and the resulting number is added to the original number, we get 143 . What can be the original numbers?

Answer 1

x is the bigger no. and y is the smaller no.
then,
x-y=3.........(1)
and
10y+x+10x+y=143
11x+11y=143
x+y=143/11=13
therefore,x+y=13
x=13-y
putting this in eq. (1)
13-y)-y=3
-2y=3-13
y=5.
putting this in eq(1) again,
x-5=3
x=8.
the original no.-..83 OR 38

Answer 2

original number
tens place = x
ones place = x + 3
number = 10x + x + 3
= 11x + 3
new number
tens place = x + 3
ones place = x
number = 10(x + 3) + x
= 10x + 30 + x
= 11x + 30
11x + 3 + 11x + 30 = 143
22x + 33 = 143
22x = 143 - 33
22x = 110
x = 110/22
x = 5
original number = 11 × 5 + 3
= 55 + 3
= 58
new number = 11 × 5 + 30
= 55 + 30
= 85