HomeMaths ProblemsA Number Consists of Two Digits. The Sum of the Digits is...

# AKIF HAMEED

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## Explanation

• 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.

Let the unit digit is z and tenâ€™s digit is y. So, number becomes â€ś10y + zâ€ť. The sum of the digits is given.

y + z = 9 ________ (i)

When 63 is subtracted then the unit digit becomes tenâ€™s digit and tenâ€™s digit becomes a unit digit.

10y + z â€“ 63 = 10z + y ________ (ii)

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

Number = ?

## Solution

Let Suppose

Unit digit = z

Tenâ€™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 â€“ 63 = 10z + y

10y â€“ y + z â€“ 10z = 63

9y â€“ 9z = 63

y â€“ z = 7 ________ (ii)

y + y + z â€“ z = 9 + 7

2y = 16

y = 8

putting in equation (i)

8 + z = 9

z = 9 â€“ 8

z = 1

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

## Conclusion

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 would be 81.