The digits of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.
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Given -
The digits of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99.
To find -
Original number
Solution -
Let the tens digit be x and the ones digit be y
Original number = 10x + y
✰ According to the first condition ✰
The digits of a 2-digit number differ by 5.
→ x - y = 5 ----(i)
✰ According to the second condition ✰
If the digits are interchanged and the resulting number is added to the original number, we get 99.
Reversed number = 10y + x
→ 10x + y + 10y + x = 99
→ 11x + 11y = 99
→ 11(x + y) = 99
→ x + y = 9 ----(ii)
Add both the equations
→ (x - y) + (x + y) = 5 + 9
→ x - y + x + y = 14
→ 2x = 14
→ x = 7
Put the value of x in eqⁿ (ii)
→ x + y = 9
→ 7 + y = 9
→ y = 9 - 7
→ y = 2
•°• Original number = 10x + y = 72
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