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
Correct Answer: 42
Solution : Distance = 21 km Let the usual speed of a motorcyclist be $x$ km/hr. Time taken, t1 = $\frac{\text{distance}}{\text{speed}}$ = $\frac{21}{x}$ When left late by $6\frac{6}{9}$ min = $\frac{1}{9}$hr, Time, t2 = travel time + waiting time = $\frac{21}{(x+12)}+\frac{1}{9}$ According to the question, $\frac{21}{x}$ = $\frac{21}{(x+12)}$ + $\frac{1}{9}$ $⇒\frac{21x+252-21x}{x(x+12)}$ = $\frac{1}{9}$ $⇒\frac{252}{x^2+12x}$ = $\frac{1}{9}$ $⇒x^2+12x =2268$ $⇒x^2+54x-42x-2268=0$ $⇒(x+54)(x-42)=0$ $⇒x=-54$ or $x = 42$ Since speed can't be negative, $x$ = 42 km/hr Hence, the correct answer is 42.
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Question : A bus left 60 minutes later than the scheduled time, but to reach its destination 48 km away in time, it had to increase the speed by 4 km/hr from the usual speed. What is the usual speed (in km/hr) of the bus?
Option 1: 9
Option 2: 12
Option 3: 15
Option 4: 8
Question : A car left 3 minutes earlier than the scheduled time and to reach the destination 126 km away in time, it has to slow its speed by 6 km/hr from the usual. What is the usual speed (in km/hr) of the car?
Option 1: 56
Option 2: 63
Option 3: 94.5
Option 4: 126
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 person covers 28 km while walking at a speed of 8 km/hr. How much distance (in km) will he cover at the same time if he walks at a speed of 6 km/hr?
Option 1: 36
Option 2: 28
Option 3: 32
Option 4: 21
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
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