Question : A man cycles at the speed of 8 km/h and reaches the office at 11 am and when he cycles at the speed of 12 km/h, he reaches the office at 9 am. At what speed should he cycle so that he reaches his office at 10 am?
Option 1: 9.6 km/h
Option 2: 10 km/h
Option 3: 11.2 km/h
Option 4: cannot be determined
Correct Answer: 9.6 km/h
Solution : Given: First speed = 8 km/h and second speed = 12 km/h The starting time will be the same in both conditions. Distance travelled by first speed in 2 hours, We know that, Distance = Speed $\times$ Time ⇒ Distance = 8 $\times$ 2 km $\therefore$ Distance = 16 km Now, the time is taken by second speed to travel a distance of 16 km, Time = $\frac{\text{distance}}{\text{second speed - first speed}}$ Time = $\frac{16}{12 -8}$ = 4 hour So, the total time taken by second speed = 4 h $\therefore$ total distance = 4 $\times$ 12 = 48 km Starting time to travel at second speed = 9 am − 4 hrs = 5 am According to the question, At 10 am, the required time to reach the office = 10 am − 5 am = 5 hrs So, required speed = Total Distance / Time ⇒ Required speed = $\frac{48}{5}$ = 9.6 km/h Hence, the correct answer is 9.6 km/h.
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