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The sum of the digit of a 2-digit number is 11 the number obtained by interchanging the digit exceed the original number by 27 find the number

Posted by Amazin Arts 6 years, 5 months ago

CBSE > Class 08 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

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 = {tex}\frac{126}{18}{/tex}
x = 7
y = 11 - x = 11 – 7 = 4
y = 4
Therefore the number is 47.

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CBSE > Class 08 > Mathematics