# 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.

Solution of Digit Problem3 to Worksheet