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Question

If 12.287287287........ can be represented in pq form, then 'p - q ' is

A
11266
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B
11176
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C
11277
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D
11276
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Solution

The correct option is D 11276
Let x = 12.287287287..... --- (i)
here the periodicity of the decimal is three.
So we multiply both sides of (i) by 1000, we get

1000x = 12287.287287287--(ii)
Subtract (i) from (ii), we have

1000x = 12287.287287287
- x = 12.287287287
----------------------------------
999x = 12275.000000000.....

x = 12275999

p = 12275 and q = 999

So, p-q = 11276.

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