Question

The sum of two digit number and the number formed by reversing the order of digits is 66.if the two digits differ by 2,find the number.How many such numbers are there?

Answer 1

let 2numbers be x,y
2 digit no. be 10x+y
reversing digits no. =10y+x
according to problem
10x+y+10y+x=66
11x+11y=66
11(x+y)=66
x+y=66/11
x+y=6. eq 1
x-y=2. eq 2
____________
2x=8
x=4
substituting x=4 in eq 1
4+y=6
y=6-4
y=2

Answer 2

let one of the digit be x (ones)
---- second---------------y (tens)
yx+xy=66----(eq 1)
y-x=2-------(eq 2)
from eq 2
y=2+x------(eq 3)
puting eq 3 in 1
(2+x)x+x(2+x)=66
2x+x2+2x+x2=66
4x+2x2=66
2x2=66-4x
now do on your own