Question

8.
The sum of a two digit number and the number obtained by interchanging the digits of the
number is 121. If the digits differ by 5, then find the number [Aryabhatta-2011]
(A) 38, 83
(B) 27, 72
(C) 39, 93
(D) 61.16​

Answer 1

A 2digit number 'xy' can be expressed as 10x+y

if digits are reversed, 'yx' can be expressed as 10y+x

given sum of digit and reversing it is 121 hence

10x+y+10y+x=121

11x+11y=121

x+y=11-------(1)

given digits differ by 5,

x-y=5----------(2)

solving (1) and (2)

x=8,y=3

hence optionA