The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number?
Hint: if there is a two digit number it means there are two places, ones and tens. For solving questions let assume the digit at once place be x and tense place be y. Then apply the condition of the question to solve further.
Complete step-by-step answer: Here in the given question there is a two digit number whose sum is 13. Now, let the digit at once place be x and tense place be y.
Then the sum of the digit is x+y=13…… let it equation (1), as in the question it is given that the sum of digit numbers is 13.
Tens place=y Once place= x
Therefore the two digit number forms by these two digits is Number= 10(y)+1(x) as we know that for forming a two digit number we multiply the digit at tens place by 10 and then add it with the digit at once place by multiplying 1 at once place. Therefore the required number is 10y+x.
Now according to question we interchange the numbers, I.e. tense place become= x and once place became=y
The new number formed is, Number= 10(x) +1(y).
Therefore new number=10x+y.
Now in the question, it says that if the number is subtracted from the one obtained by interchanging the digits, the result is 45.
i.e. 10x+y-(10y+x) =45 $ \Rightarrow 9x - 9y = 45$ Take 9 common and divide it to the right hand side. $ \Rightarrow x - y = 5$……….let it equation (2) On adding (1) and (2) we get, 2x=18 $\therefore x = 9$ Now put the value of x in equation (1) we get, 9+y=13 $\therefore y = 4$ Therefore the two digit number$ = 10y + x = 10 \times 4 + 9 = 49$. Hence, the required number is 49.
Note: Whenever we face such a type of question the key concept for solving the question is first assume the digits at once place be x and tense place be y and then form the numbers by these digits according to the question. And then apply the statement of question to proceed a d then we will find the value of that digit. Now put the value of that digit to get the number.