Solution of Digit Problem3

In this page solution of digit problem3 we are going to see solution for question 5 and question 6 with detailed steps.

Question 5:

The number consists of two digits whose sum is 9. If 45 is added to the number, the digits are reversed. Find the number.

Solution:

Let "x y"  be the required two digit number.

The sum of its digits = 9

                     x + y = 9   --------- (1)

If 45 is added to the number, the digits are reversed.The given number is x y and its reversed digits is y x.

                 x y + 45 = y x

Let us write this as expanded form. In "x y" x is in the place of ten's and y is in the place of one's. Like that in "y x" y is in the place of ten's and x is in the place of one's.

        10 x + y + 45 = 10 y + x

        10 x - x + y - 10 y = - 45

             9 x - 9 y = - 45

Divide this equation by 9.

             x - y = - 5 --------- (2)

By solving these two equations we will get the value of x and y.

              x + y = 9   --------- (1)

              x - y = -5   -------- (2)

(1) + (2)    x + y = 9

                x - y = -5 

             __________

               2 x = 4

                 x = 4/2

                 x = 2

Substituting x = 2 in the first equation 

                2 + y = 9

                 y = 9 - 2

                 y = 7

Therefore the required number is 27


Checking:

Sum of its digits = 9

 2 + 7 = 9

If 45 is added to the number, the digits are reversed.

27 + 45  =  72


These are the problems in solution of digit problem3.



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