Question : A car covers a certain distance in 25 hours. If it reduces the speed by $\frac{1}{5}$th, the car covers 200 km less in that time. The speed of the car is:
Option 1: 60 km/hr
Option 2: 30 km/hr
Option 3: 40 km/hr
Option 4: 50 km/hr
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Correct Answer: 40 km/hr
Solution : Time taken, $t = 25$ hours Let the initial distance be $d$ and the initial speed be $s$. Speed = Distance ÷ Time $s = d ÷ t$ $⇒t = \frac{d}{s}$---------------(i) When $s$ is reduced by $\frac{s}{5}$, new $s = \frac{4s}{5}$ and $d = d - 200$, $t = \frac{d - 200}{ \frac{4s}{5}}$ -----------------(ii) From (i) and (ii), $\frac{d}{s}$ = $\frac{d - 200}{ \frac{4s}{5}}$ $⇒\frac{4d}{5} = d - 200$ $⇒4d = 5d - 1000$ $⇒d = 1000$ km $\therefore$ Speed, $s= \frac{d}{t}$ = $\frac{1000}{25}$ = 40 km/hr Hence, the correct answer is 40 km/hr.
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Question : Vikas covered a certain distance by bike. If he covers 40% of the distance at 40 km/hr, 50% of the distance at 25 km/hr and the remaining 10% distance at 10 km/hr. Find his average speed over the whole distance.
Option 1: 25 km/hr
Option 2: 28 km/hr
Option 3: 26 km/hr
Option 4: 30 km/hr
Question : To cover a certain distance at a speed of 60 km/hr, a train takes 15 hours. If it covers the same distance in 12 hours, what will its speed be?
Option 1: 65 km/hr
Option 2: 70 km/hr
Option 3: 75 km/hr
Option 4: 80 km/hr
Question : A boat goes a certain distance at 30 km/hr and comes back the same distance at 60 km/hr. What is the average speed (in km/hr) for the total journey?
Option 1: 45 km/hr
Option 2: 50 km/hr
Option 4: 35 km/hr
Question : A car covers a distance of 350 km in 5 hours and covers another 450 km at a speed of 90 km/hr. What is the average speed (in km/hr) of the car?
Option 1: 72
Option 2: 82
Option 3: 80
Option 4: 85
Question : A car starts from point A towards point B, travelling at the speed of 20 km/hr. $1\frac{1}{2}$ hours later, another car starts from the point and travels at the speed of 30 km/hr and reaches $2\frac{1}{2}$ hours before the first car. Find the distance between A and B.
Option 1: 300 km
Option 2: 240 km
Option 3: 260 km
Option 4: 280 km
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