Question

A number consists of two digits,the sum of the digits is 10.If 36 is added to the number, the place of digits is interchanged .Find the number​

Answer 1

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let unit digit is y

ten's digit is x

Number becomes 10x+y

given:x+y=10->equation 1

if digits are interchanged number becomes 10y+x

36+number=new number

36+10x+y=10y+x

9(x-y)=-36

x-y=-4->equation 2

from equations 1,2

x=3,y=7

SO NUMBER IS 37

Answer 2

Answer:

Well, let the tens place and ones place digits in the number be respectively a and b , which are each between 0 and 9 inclusive. Then the number itself is equal to 10a+b . Now add 36 to the number, and we have 10a+b+36=10b+a , where the last part of the equality follows from the reversal of the digits.

The above equation simplifies to 9a+36=9b .

This simplifies to 9(a+4)=9b , or a+4=b .

We need a second equation in order to get a unique solution. The original question says that “the sum of the two-digit number is 10.” This is poorly-worded, but I think what it means is that the sum of the digits in the two-digit number is 10. If that’s true, then a+b=10 . Since a+4=b, this becomes 2a+4=10 . I.e. 2a=6 , or a=3 . Thus b=a+4=7.

The number is 37. Check this answer:

37+36=73

which is indeed a reversal of the digits.