In this page solution of digit problem2 we are going to see solution for question 3 and question 4 with detailed steps.

**Question 3:**

The unit's digit of a two digit number is twice its ten's digit. If 18 is added to the number, the digits interchange their places. Find the number.

**Solution:**

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

Let "x" be the number which is in unit's digit

Let "y" be the number which is in ten's digit

The unit's digit of a two digit number is twice its ten's digit

y = 2 x

2x - y = 0-------(1)

x y + 18 = y x

Let us write them using expanded form

10 x + y + 18 = 10 y + x

10 x - x + y - 10 y = -18

9 x - 9 y = -18

Dividing this equation by 9

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

(1) - (2) 2x - y = 0 ------(1)

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

(-) (+) (+)

_____________

x = 2

Substituting x = 2 in the first equation

2 (2) - y = 0

4 - y = 0

- y = -4

y = 4

Therefore the required number is **24**

**Checking:**

**The
unit's digit of a two digit number is twice its ten's digit. **

**2 (2) = 4**

**If 18 is
added to the number, the digits interchange their places **

**24 + 18 = 42 **

These are the problems in solution of digit problem2.

**Question 4:**

The sum of the digits of two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.

**Solution:**

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

The sum of the digits of two digit number = 12

x + y = 12 ------(1)

If the new number formed by reversing the digits is greater than the original number by 54

y x = x y + 54

Let us write this as expanded form

10 y + x = 10 x + y + 54

x - 10 x + 10 y - y = 54

- 9 x + 9 y = 54

Dividing this equation by 9. We will get

- x + y = 6 ------(2)

(1) + (2) x + y = 12

- x + y = 6

___________

2 y = 18

y = 18/2

y = 9

Substituting y = 9 in the first equation.

x + 9 = 12

x = 12 - 9

x = 3

Therefore the required number is **39**

**Checking:**

**The
sum of the digits of two digit number is 12**

**3 + 9 = 12 **

**If the new number formed
by reversing the digits is greater than the original number by 54 **

**93 = 39** **+ 54**