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 car travels with a speed of 21 m/sec in the first 10 minutes, 9.0 km in the next 10 minutes and 10 km in the last 10 minutes of its journey. What is the average speed of the car in km/hr during its entire journey?
Option 1: 60.0 km/hr
Option 2: 63.2 km/hr
Option 3: 62.0 km/hr
Option 4: 65.3 km/hr
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