What are you looking for? Let’s dig in quickly
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.
