A) \[31\frac{5}{6}\] min
B) \[32\frac{8}{11}\]-min
C) \[33\frac{8}{11}\] min
D) \[34\frac{5}{6}\]min
Correct Answer: B
Solution :
55 min are gained by minute hand in 60 min 60 min will be gained by minute hand in \[\left( \frac{60}{50}\times 60 \right)\] min \[=\frac{720}{11}\,\,\min =65\frac{5}{2}\,\min \] Thus, the hands of a correct clock coincide every \[65\frac{5}{2}\,\min .\] But the hands of the clock in question coincide every 64 min. \[\therefore \] In every 64 min, the clock in question gains \[1\frac{5}{11}\,\,\min \] In 24 h, the clock in question gains \[=\left( \frac{16}{11}\times \frac{1}{64}\times 24\times 60 \right)\] min\[=\frac{360}{11}\] min \[=32\frac{8}{11}\] min.
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