## Table of Contents – A Number Consists of Two Digits | Solution | Problem Solved

- A number consists of two digits.
- The sum of the digits is 9.
- If 63 is subtracted from the number.
- Its digits are interchanged.
- The number can be figure out in this way.

## Important Points to Solve the Problem

Let the unit digit is z and ten’s digit is y. So, number becomes “10y + z”. The sum of the digits is given.

y + z = 9 ________ (i)

When 63 is subtracted then the unit digit becomes ten’s digit and ten’s digit becomes a unit digit.

10y + z – 63 = 10z + y ________ (ii)

Solving (i) and (ii) simultaneously we can easily figure out the required number.

## To Find

Number = ?

## Solution

Let Suppose

Unit digit = z

Ten’s digit = y

Number = 10y + z

According to the first condition of the question

y + z = 9 ________ (i)

According to the second condition of the question

10y + z – 63 = 10z + y

10y – y + z – 10z = 63

9y – 9z = 63

y – z = 7 ________ (ii)

By adding (i) and (ii)

y + y + z – z = 9 + 7

2y = 16

y = 8

putting in equation (i)

8 + z = 9

z = 9 – 8

z = 1

**Number = 10y + z = 80 + 1 = 81 answer**

## Conclusion

To read more about the Number Theory: Please Click Here

It’s very helpful for the preparation of exams I recommend you must visit here if you want a detailed answer

Thank you very much.