Question

7. The sum of two digits of a two-digit number is 10. If the number obtained on reversing
the digits is 54 less than the original number, find the original number.
​

Answer 1

Step-by-step explanation:

Let unit digit is x

and ten's digit is y

Then, Original no.= x+10y

Reversing the digits=>

New no. = 10x + y

10x + y = x + 10y - 54

10x - x +y - 10y = -54

9x - 9y = -54

9(x-y) = -54

x - y = -6 - eq1

x+ y =10- eq2

Add eq 1 and eq2

2x = 4

x = 2

So, y = 8

Therefore

Original Number = 82