Answer:
Number is 61 or 16
Step-by-step explanation:
Let x be the digit at tens place and y be the digit at ones place.
So, the two digit number is 10x+y.
When the digits are reversed, number becomes 10y+x
According to question, the sum of a 2-digit number and the 2-digit number when the digits are reversed is 77
10x+y+10y+x=77
11x+11y=77
x+y=7 (i)
Also, difference of the same two numbers is 45
(10x+y)-(10y+x)=45 or (10y+x)-(10x+y)=45
x-y=5 (ii) or y-x=5 (iii)
Consider equations (i) and (ii)
Put x=y+5 in x+y=7
y+5+y=7
2y=2
y=1
So, x=y+5=1+5=6
So, number = 10x+y=10(6)+1=61
Consider equations (ii) and (iii)
Put y=x+5 in x+y=7
x+5+x=7
2x=2
x=1
So, y=x+5=1+5=6
So, number = 10(1)=6=16
Therefore, number is 61 or 16
