Question : A boy increases his speed to $\frac{9}{5}$th times of his original speed. By doing this, he reaches his school 40 minutes before the usual time. How much time (in minutes) does he usually take?
Option 1: 120
Option 2: 30
Option 3: 90
Option 4: 45
Correct Answer: 90
Solution : Let the speed of the boy be $x$ km/hr. Initial time = $t$ So, distance = $tx$ New time = $t-40$ New speed = $x × (\frac{9}{5})=\frac{9x}{5}$ According to the question, $tx=(t-40)\frac{9x}{5}$ $⇒5t=9t-360$ $⇒ 4t=360$ $\therefore t =90$ minutes Hence, the correct answer is 90.
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Question : If Abhi travels a certain distance at 6 km/hr, he reaches his destination 12 minutes early, but if he travels at 4 km/hr, he reaches his destination 10 minutes late. The speed (in km/hr) at which he should travel to reach his destination on time is _____.
Option 1: $5 \frac{1}{4}$
Option 2: $5 \frac{1}{8}$
Option 3: $4 \frac{3}{7}$
Option 4: $4 \frac{5}{7}$
Question : A motorcyclist left $6\frac{6}{9}$ minutes later than the scheduled time but to reach its destination 21 km away on time, he had to increase his speed by 12 km/hr from the usual speed. What is the usual speed (in km/h) of the motorcyclist?
Option 1: 28
Option 2: 35
Option 3: 42
Option 4: 64
Question : A vehicle is going at one-fourth of its usual speed and it takes an extra 45 minutes to reach its destination. It's usual time to cover the same distance is:
Option 1: 15 minutes
Option 2: 10 minutes
Option 3: 30 minutes
Option 4: 20 minutes
Question : A person takes 40 minutes more than his usual time when he covers a distance of 20 km at 5 km/hr. If he covers the same distance at 8 km/hr, he takes $x$ minutes less than the usual time. What is the value of $x$?
Option 1: 48
Option 2: 54
Option 3: 45
Option 4: 50
Question : A takes 2 hours 30 minutes more than B to walk 40 km. If A doubles his speed, then he can make it in 1 hour less than B. What is the average time taken by A and B to walk a 40 km distance?
Option 1: 7 hours 15 minutes
Option 2: 5 hours 45 minutes
Option 3: 6 hours
Option 4: 5 hours 15 minutes
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