| Direction: Select the missing number from the given responses. |
A) \[10\frac{10}{11}\] min past 5
B) \[43\frac{7}{11}\] min past 5
C) Both 'a' and 'b'
D) None of these
Correct Answer: C
Solution :
At 5 o'clock the minute hand will be 25 min spaces behind the hour hand. Now, when the two hand are at right angle, they are 15 min spaces apart. So, there are two cases. Case 1 When the minute hand is 15 min spaces behind the hour hand. To be in this position, the minute hand will have to gain \[\text{(}25-15\text{) }=\text{ }10\] min spaces. Now, 55 min spaces are gained in 60 min \[\therefore \] 10 min spaces are gained in \[\left( \frac{60}{55}\times 10 \right)\,\min =\frac{120}{11}\min \] \[5+3\times \frac{2}{3}-4=3\text{ }or\text{ }3=3,\] They are at right angle at \[10\frac{10}{11}\min \] past 5. Case 2 When the minute hand is 15 min spaces ahead of the hour hand. To be in this position, the minute hand will have to gain \[(25+15)=40\,\min \] spaces. Now, 55 min spaces are gained in 60 min \[\therefore \] 40 min spaces will be gained in \[\left( \frac{60}{55}\times 40 \right)\min \] \[=\frac{480}{11}\min =43\frac{7}{11}\min \] So, they are at right angle at \[43\frac{7}{11}\min \] past 5.
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