Question

The sum of two digit number and the number formed by reversing the digits is 55. find the number if one of the digits is one more than other

Answer 1

let the 2 digits be x and y. so
xy+yx=55
10x+y+10y+x=55
11x+11y=55
x+y=5. (1)
Also we know one number is 1 greater than the other. Assume x is 1 greater than y. Then,
x=y+1
Substituting in (1):
y+1+y=5
y=2
So, x=3
Similarly assume y is greater. We get x=2 and y=3. So the number can be 23 or 32.

Answer 2

Let the two digits of the number be x and y.
Then the number will be 10x + y.
The question says that 10y + x + 10x + y = 55
= 11x + 11y = 55 .....(1)
By dividing eq(1) by 11 we get
x + y = 5 .....(2)
Also, x = y+1
x - y = 1 ......(3)
On doing (2) - (3) We get,
2y = 4
y = 2 Put this value in eq (2)
x + y = 5
x + 2 = 5
x = 5 - 2
x = 3
So the number is 10*(3) + 2 = 30 + 2 = 32.
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