In this page solution of digit problem1 we are going to see solution for question 1 and question 2 with detailed steps.

**Question 1:**

The sum of digits of a two digit numbers is 15 and if 9 is added to the number the digits are interchanged. Find the required number.

**Solution:**

Let "x y" be the required two digit number. Here "x" is in ten's place and "y" is in unit place

The sum of digits of a two digit number = 15

x + y = 15 ------(1)

If 9 is added to the number the digits are interchanged

x y + 9 = y x

Now let us write this number in expanded form

10 x + y + 9 = 10y + x

10 x - x + y - 10 y = -9

9x - 9y = -9 ------(2)

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

(1) x 9 => 9 x + 9 y = 135

(1) + (2) 9 x - 9 y = -9

______________

18 x = 126

x = 126/18

x = 7

Substituting x = 7 in first equation

7 + y = 15

y = 15 - 7

y = 8

Therefore the required number is **78**

**Checking:**

**The sum of digits of a two digit number is 15.**

**Answer 78 is satisfying this condition. Because 7 + 8 = 15**

**If 9 is added to the number the digits are interchanged**

**That is 78 + 9 = 87**

**Question 2:**

The sum of the digits of a two digit number is 10. If the number formed by reversing the digits is less than the original number by 36,find the required number.

**Solution:**

Let "x y" be the required two digit number. Here "x" is in ten's place and "y" is in unit place.

The sum of the digits of a two digit number = 10

x + y = 10 --------(1)

If the number formed by reversing the digits is less than the original number by 36.

y x = x y - 36

Let us write these as expanded form

10 y + x = 10 x + y - 36

x - 10 x + 10 y - y = - 36

- 9 x + 9 y = - 36

By divide this equation by 9 we will get

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

(1) + (2) x + y = 10

- x + y = -4

___________

2 y = 6

y = 6/2

y = 3

Substituting y = 3 in the first equation

x + 3 = 10

x = 10 - 3

x = 7

Therefore the required number is **73**.

**Checking:**

**The sum of digits of a two digit number is 10.**

**Answer 73 is satisfying this condition. Because 7 + 3 = 10**

**If the number formed by
reversing the digits is less than the original number by 36.**

**That is 37 = 73 - 36** solution of digit problem1

These are the problems in solution of digit problem1.