Question

The sum of the digits of a two digit number is 9. If the digits are reversed, the number is increased by 45. Find the original number.

Answer 1

the answer of this ques is 27
as

2+7=9
(sum of the two digits is 9)
27+45=72
(inverted form  of 27 is 72)

Answer 2

Hello !
Let the digits be x at the tens place and y at the ones place,
According to the question ,
x+y = 9                       ...........................  eqn. 1
and,
the number is 10x+y
so,
10x+y+45 = 10y+x     ........................... eqn. 2
Solving the eqn 2 ;
10x-x- 10y+y=45
⇒ 9x - 9y = 45
⇒ 9(x-y) = 45
⇒ x - y = 5                   ........................... eqn. 3
On adding the eqn. 1 and eqn. 3 we get,
2x = 14
⇒  x = 7                             Ans.
On substituting the value of x in the 1st eqn we get ,
7+y=9
⇒ y = 2                               Ans.
Hence, the original number is 72.
I hope it is correct !
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