sum of digits of 2 digit no. is 10 . the no. obtained by interchanging the no. exceeds the origional no. by 30 . find the original no.
Answers
Answer:
37 is the number when the difference between original and interchanged-digits no. is 36.
Step-by-step explanation:
There is no such 2 digit number whose sum of digits is 10 and when interchanged, exceed the original by 30.
The question is valid by exceeding the new number from the original by 36.
Let the digits of the number be x and y.
Acc. to ques, x + y = 10 --(i)
So, the number will be 10x + y. (I have taken x to be the tens digit)
Now, acc. to ques, the no. obtained by interchanging the no. exceeds the original no. by 30.
=> 10y + x = 10x + y + 36
=> 10y - y + x - 10x = 36
=> 9y - 9x = 36
=> y - x = 4 --(ii) (Dividing whole equation by 9)
Adding (i) and (ii),
x + y = 10
y - x= 4
=> 2y = 14
∴ y = 14/2 => 7
Putting this in (i),
x + y = 10
=> x + 7 = 10
∴ x = 10 - 7 => 3
Thus, the number whose sum of digits is 10, the no. obtained by interchanging the original no. exceeds the original by 30, is 37.