Question

the difference of the digit of a two digit number is 3 if the digit are interchange and new number is added to original number the result is 77 find the original number​

Answer 1

Answer:

Let the number be 10x+y where x is in tens place and y at ones place. Here, 10y +x is a reversed number.

First condition,

x - y = 3............(1)

Second condition,

10x+y +10y +x = 77

or, 11x + 11y = 77

or, 11(x+y) = 77

or x + y = 7............(2)

adding (1) and (2),

2x = 10 or x=5

substituting  value of x in equation (2) ,

5 + y = 7

or y = 2

So, the original number = 10x +y = 1o × 5 +2 = 52

Step-by-step explanation:

Answer 2

Answer:

The original number is 52.

Step-by-step explanation:

As we have studied from beginning that any  digit or number can be taken in the form of a variable whether id x, a, b, y etc.

Also, We all know that any two digit number can be written in the form of (a×10)+b which directly mean ab [taken a 2 as 'a' and 4 as 'b', which equals to 24]

Now, Coming on the question :-

let the unit digit be x.

and tens digit can be x+3  [As they differ by 3]

so, the equation for the original number is (x+3)10 + x

after interchanging the unit and tens digit we'll get:(x)10 + x + 3

In the question we have given that the interchanged and the original sums 77. By this we got an equation :-

10(x+3) + x + (x)10 + x+3

solution :-

10(x+3) +x + (x)10 + x+ 3 = 77

10x + 30 + x + 10x + x + 3 = 77

22x + 33 = 77

22x = 77- 33

x = 44/22

x = 2   [unit digit]

we found that the x or the unit digit is 2.

by our above expression it comes out that number is 52.

here's how -

our expression was (x + 3)10 + x

                               = (2 + 3)10 + 2

                               = 50 + 2

                               = 52

Verification :-

we have given that original and interchanged numbers sums 77.

52 + 25 = 77