The sum of a two digit number and the number formed by reversing the order of digits is $154,$ two digits differ by $4,$ find the number.

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Solution

Difference btw the 2 digits=4
Let one digit be x and the other will be x+4 (it can also be x-4. Either is correct)
the no.=10x +x+4
By reversing the digits, the no.= 10(x+4) +x
The sum = (10x +x+4)+(10x +40+x)
=11x+4+11x+40
22x+44=154
22x=154-44
22x=110
x=110÷22
Implies that,x=5
The no.=(10×5)+(5+4)
=50+9
The no. is=59

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