Question

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Answer 1

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Answer 2

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Answer...

Let the number at tens place be x while that at ones place be y

Given →

x + y = 9 ..... eq.(1)

$\bold{\underline{Original\: number}}$ →

10x + y

$\bold{\underline{Number\: after\: interchanging\: digits}}$ →

10y + x

A.T.Q →

9(10 x + y) = 2(10 y + x)

90 x + 9y = 20 y + 2x

88 x - 11 y = 0 ..... eq(2)

multiplying eq(1) by 11 ,

11 x + 11 y = 99 ....... eq(3)

adding eq(2) and eq(3), we get

99 x = 99

$\boxed{x = 1}$

putting this value in eq(1),

1 + y = 9

$\boxed{y = 8}$

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