Question : The ratio of the distance between two places A and B to the distance between places B and C is 3 : 5. A man travels from A to B at a speed of $x$ km/hr and from B to C at a speed of 50 km/hr. If his average speed for the entire journey is 40 km/hr, then what is the value of $(x - 10) : (x + 1)$?
Option 1: 11 : 10
Option 2: 20 : 31
Option 3: 31 : 20
Option 4: 10 : 11
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Correct Answer: 20 : 31
Solution : According to the question Let the distance from A to B is $3a$ and from B to C is $5a$ Time Taken by man to travel from A and B at a speed of $x$ km/hr = $\ \frac {3a}{x}$ Time Taken by man to travel from B and C at a speed of 50 km/hr = $\frac{5a}{50}$ = $\frac{a}{10}$ Average speed = $\frac{\text{Total distance}}{\text{Total time}}$ ⇒ $\frac{3a + 5a}{\frac{3a}{x} + \frac{a}{10}}$ = 40 ⇒ $\frac{8a}{\frac{3a}{x} + \frac{a}{10}}$ = 40 ⇒ $8a = 40a(\frac{3}{x} + \frac{1}{10}$) ⇒ $\frac{1}{5}$ = $\frac{(30 + x)}{10x}$ ⇒ 2$x$ = 30 + $x$ ⇒ $x$ = 30 km/h Value of ($x - 10) : (x + 1) = (30 – 10) : (30 + 1) = 20: 31$ Hence, the correct answer is 20 : 31.
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Question : A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately:
Option 1: 10.4 km/hr
Option 2: 10.8 km/hr
Option 3: 11.0 km/hr
Option 4: 12.2 km/hr
Question : A car travels a certain distance at 70 km/hr and comes back at 30 km/hr. Find the average speed for the total journey.
Option 1: 42 km/hr
Option 2: 50 km/hr
Option 3: 34 km/hr
Option 4: 58 km/hr
Question : Reshma covers 45 km at a speed of 15 km/hr by bicycle, 80 km at a speed of 40 km/hr by car, and another 6 km at a speed of 2 km/hr on foot. Find her average speed for the whole journey (correct to 2 decimal places).
Option 1: 16.38 km/hr
Option 2: 43.50 km/hr
Option 3: 18.36 km/hr
Option 4: 15.25 km/hr
Question : A man travels some distance at a speed of 12 km/hr and returns at a speed of 9 km/hr. If the total time taken by him is 2 hours and 20 minutes, the distance is:
Option 1: 35 km
Option 2: 21 km
Option 3: 9 km
Option 4: 12 km
Question : A jeep travels to a place 300 km away at an average speed of 60 km/hr and returns at a speed of 30 km/hr. What is the average speed (in km/hr) for the whole journey?
Option 1: 75
Option 2: 80
Option 3: 40
Option 4: 60
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