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the answer is 72
7+2 = 9
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GIVEn
Sum of a two digit number is 9. The number obtained by interchanging the digit exceeds the given number by 27
TO FINd
Find the original number
SOLUTIOn
✯ Let the tens digit be x and ones digit be y
- Required number = 10x + y
- Number obtained by interchanging the digit = 10y + x
✞ According to the given condition
- x + y = 9 --(i)
✯ The number obtained by interchanging the digit exceeds the given number by 27
→ 10y + x = (10x + y) + 27
→ 10y + x = 10x + y + 27
→ 10y - y + x - 10x = 27
→ 9y - 9x = 27
→ 9(y - x) = 27
→ y - x = 27/9
→ y - x = 3 --(ii)
✞ Add both the equation
→ (x + y) + (y - x) = 9 + 3
→ x + y + y - x = 12
→ 2y = 12
→ y = 12/2 = 6
✞ Put the value of y in eqⁿ (ii)
→ y - x = 3
→ 6 - x = 3
→ x = 6 - 3
→ x = 3
∴ x = 3 & y = 6
Hence, the required number
→ 10x + y
→ 10*3 + 6 = 30 + 6 = 36
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