A) 14
B) 55
C) 69
D) None of these
Correct Answer: C
Solution :
Sol. [c] Let. \[x=0.2\overline{54},\] |
then \[x=0.2545454......\] ...(1) |
Multiplying eq. (1) by 100. we get |
\[100\text{x}=\text{25}.\text{4545}..........\] ...(2) |
Subtracting eq. (1) from eq. (2). we get |
\[99x=25.2\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,x=\frac{252}{990}=\frac{14}{55}\] |
Comparing with \[\frac{p}{q},\]we get |
\[p=14\] |
and \[q=55\] |
Hence, \[\text{p}+\text{q}=\text{14}+\text{55}=\text{69}\] |
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