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A Number Consists of Two Digits. The Sum of the Digits is 9. If 63 is Subtracted from the Number, its Digits are Interchanged. Find the Number.

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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 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

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.

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