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Question

The number x=1.242424.... can be expressed in the form x=pq, where p and q are positive integers having no common factors. Then p+q equals ____.

A
72
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B
74
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C
41
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D
53
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Solution

The correct option is D 74
Given, x=1.24242 .....(1)
100x=124.2424 ....(2)
Substract eqn (1) from eqn (2), we get
99x=123x=12399=4133
Here p=41 and q=33
Thus p+q=41+33=74

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