 Answer 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=yOnce place= xTherefore 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=yThe 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. |
The sum of digits of a two digit number is 13 if sum of their squares is 89 find the number
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