Question

the sum of a 2 digit number and the number obtained by reversing the digit is 77 if the digits of the number differ by 3 find the number

Answer 1

let the req. no.s unit digit be y and tens be x
A.C.Q 
(10x+y)+(10y+x)=77
11x+11y=77
11(x+y)=77
x+y=7-------------------------------------exn. 1
x-y=3---------------------------------------exn. 2
x=3+y-------------------------------------exn. 3
substituting exn. 3 in exn. 1
3+y+y=7
2y=7-3
y=4/2
y=2
from exn. 2
x-2=3
x=5
no. is 53