The sum of the digits ofa 2 digit number is 11. The number obtained by interchanging the digits exceeds the
original number by 27. Find the number.
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Answer:
The given “two-digit number” is found to be 47
Step-by-step explanation:
Let the number in one’s place be x and the number in ten’s place be y such that the number is yx.
Given that x + y = 11
y = 11 – x
Thus the number
= 10 y + x
= 10(11 – x) + x = 110 – 10x +x = 110 – 9x
After interchanging, the number becomes
= 10x + y
= 10(x) + (11 – x) = 11 + 9x
Given that after interchanging the number exceeds by 27.
11 + 9x = 110 – 9x + 27
9x + 9x = 110 – 11 + 27
18x = 126
x = 126/18
x = 7
y = 11 - x = 11 – 7 = 4
y = 4
Therefore the number is 47.
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