AFCAT I 23 Jan 2025 Shift 2 Paper

Let xy be the two-digit number.
The two-digit number xy can be written as =10x+y
The interchanged two-digit number =yx=10y+x
According to the question,
‌⇒10x+y−(10y+x)=45
‌⇒10x+y−10y−x=45
‌⇒9x−9y=45
‌⇒x−y=5
Now,
The product of the digits of the original number =x×y=14
Since (a+b)2−(a−b)2=4ab
Therefore,
‌⇒(x+y)2−(x−y)2=4xy
‌⇒(x+y)2−(5)2=4×14
‌⇒(x+y)2−25=56
‌⇒(x+y)2=81
‌⇒(x+y)=9
Therefore,
The sum of the digit of the original number =9
∴ The required answer is 9 .