Question : A person covers a distance of 300 km and then returns to the starting point. The time taken by him for the outward journey is 5 hours more than the time taken for the return journey. If he returned at a speed of 10 km/hr more than the speed of going, what was the speed (in km/hr) for the outward journey?
Option 1: 15
Option 2: 20
Option 3: 30
Option 4: 25
Correct Answer: 20
Solution : Let the speed of the forward journey be $x$ km/hr. Speed of return journey will = $(x + 10)$ km/hr Time taken in return journey = $\frac{300}{(x + 10)}$ hours Time taken in forward journey = $\frac{300}{x}$ hours According to the question, ⇒ $\frac{300}{x} -\frac{300}{x+10} = 5$ ⇒ $\frac{300(x + 10) - 300x}{x(x + 10)} = 5$ ⇒ $300x + 3000 - 300x = 5x^2+50x$ ⇒ $3000 = 5x^2 + 50x$ ⇒ $5x^2 + 50x - 3000 = 0$ ⇒ $x^2 + 10x - 600 = 0$ ⇒ $x^2 + 30x - 20x - 600 = 0$ ⇒ $x(x + 30) - 20(x + 30) = 0$ ⇒ $(x - 20)(x + 30) = 0$ As speed cannot be negative, so $x=20$ km/hr Hence, the correct answer is 20.
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Question : A person travels a distance of 300 km and then returns to the starting point. The time taken by him for the outward journey is 5 hours more than the time taken for the return journey. If he returns at a speed of 10 km/hr more than the speed of going, what is the average speed (in km/hr) for the entire journey?
Option 1: 20
Option 2: 15
Option 3: 24
Option 4: 30
Question : A man covers a certain distance by bike. If he covers 25% of the distance at the speed of 25 km/hr, 50% of the distance at the speed of 50 km/hr and the remaining distance at the speed of 12.5 km/hr, find his average speed over the whole journey.
Option 1: 20 km/hr
Option 2: 30 km/hr
Option 3: 25 km/hr
Option 4: 35 km/hr
Question : The speed of a boat in standing water is 6 km/hr and the speed of the stream is 2.5 km/hr. A man rows to a place at a distance of 59.5 kilometres and comes back to the starting point. The total time taken by him is:
Option 1: 16 hours
Option 2: 24 hours
Option 3: 22 hours
Option 4: 18 hours
Question : A boy goes from home to school at a speed of 30 km/hr and returns back at a speed of 70 km/hr. What is his average speed for the journey?
Option 1: 42 km/hr
Option 2: 48 km/hr
Option 3: 38 km/hr
Option 4: 36 km/hr
Question : A car completed a journey of 400 km in $12\frac{1}{2}$ hours. The first $\frac{3}{4}$th of the journey was done at 30 km/hr. Calculate the speed for the rest of the journey.
Option 1: 45 km/hr
Option 2: 25 km/hr
Option 3: 40 km/hr
Option 4: 30 km/hr
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