Question

the sum of the digit of a 2 digit number is 10. the number obtained by interchanging the digits exceeds the original number by 36 . find the original number .​

Answer 1

original number=xy

their sum, x+y=10...........(1)

on interchanging the number

(10y+x)=(10x+y)+36

9y-9x=36

y-x=4........................(2)

adding (1) & (2) we get

2y=14

y=7

putting the value of y in (1) we get

x=3

the original number is xy i.e. 37

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Answer 2

Answer: Original number is 37

Step-by-step explanation:Firstly we have rewrite the word problem into Mathematical form:  

Let's assume :

x = the 10's digits

y = units

Then the original number:  

10x + y = two digit number

Now lets write down what's given in the problem:  

x + y = 10  

Re-written as: y= 10 -x (equation 1)

We are also told the number obtained by interchanging the two digits exceeds the number by 36:

interchanged = original + 36

10y + x = 10x + y + 36

9y = 9x + 36

y = x + 4

Now equate the above equation to equation 1  

10 - x = x +4

2x = 6

x = 3

Now find y:

x+ y =10

y= 10 - 3

y = 7

Now we are required to find the original number. From above the equation of the original number is:  

10x + y = 10(3) + 7 =37

The original number is 37