xy is a number that is divided by ab where xy < ab and gives a result 0.xyxyxy... then ab equals

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Solution

The correct option is C 99
The sequence 0.xyxyxyxy... can be written as:
$(x y \div 100) + (x y \div 10000) + (x y \div 1000000) + . . .$
$= (x y \div 100) \times (1 + 1 \div 100 + 1 \div 10000 + . . . .)$ [The second part is a geometric series with ratio 1/100]
$= (x y \div 100) \times 1 \div (1 - 1 \div 100)$
$= x y \div 99$
as $x y \div a b = 0. x y x y x y x y . . . = x y \div 99$
$a b$ is $99$

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