Question

the sum of a 2 digit number is 10 if we reverse the digits the new number will be 54 more than original number what is the original number

Answer 1

the answer for the question given above is 82 as the sum of the digits is10(8+2) , the number when reversed=28(82), the difference also is 54 (82-28)

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Answer 2

Let the tens place digit be x and unit place be y
sum of numbers = x+y = 10 ...(1)
Original number = 10x +y
According to the question
10x+y+54 = 10y+x
10x-x+y-10y = -54
9x-9y= -54
x-y = -6 .......(2)
Add equation (1) and equation(2) we get
2x =4
x = 4/2
x=2
Put the value of x=2 in equation (1)
2+y=10
y=10-2
y=8
Original Number 10x+y =10(2)+8=28