Arithmetic aptitude :: Time and Distance :: General Questions

• Time and Distance - General Questions
• Time and Distance - Data Sufficiency 1
• Time and Distance - Important Formulas and Facts

1. Speed $=\left(\frac{Distance}{Time}\right)$, Time $=\left(\frac{Distance}{Speed}\right)$, Distiance $=(Speed\times Time)$

2. $x$ km/hr $=\left(x\times\frac{5}{18}\right)$ m/sec

3. $x$ m/sec $=\left(x\times\frac{18}{5}\right)$

4. If speed ratios of X and Y is $x:y$, then the time ratio by them to cover same distance $=\frac{1}{x}:\frac{1}{y}$ or $y:x$

5. Suppose an object covers a certain distance at $x$ km/hr and an equal distance at $y$ km/hr. Then, the average speed of during the

whole travel is $\left(\frac{2xy}{x+y}\right)$ km/hr.

A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling ?

Answer:

Explanation:

Number of gaps between 21 telephone posts = 20.

Distance travelled in 1 minute $=(50\times 20)$ m = 1000 m = 1 km.

$\therefore$ Speed = 60 km/hr.

Which of the following trains is the fastest ?

Answer:

Explanation:

25 m/sec $=\left(25\times \frac{18}{5}\right)$ km/hr = 90 km/hr

And, 25 m/sec $=(25\times 60)$ m/min = 1500 m/min. So, all the three speeds are equal.

A walk a certain distance and ride back taking a total time of 37 minutes. A could walk both ways in 55 minutes. How long would it take me to ride both ways ?

Answer:

Explanation:

Let the distance be $x$ km. Then,

(Time taken to walk $x$ km) + (Time taken to ride $x$ km) = 37 min.

$\Leftrightarrow$ (Time taken to walk $2x$ km) + (Time taken to ride $2x$ km) = 74 min.

But, time taken to walk $2x$ km = 55 min.

Time taken to ride $2x$ km $=(74-55)$ min = 19 min.

A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train ?

Answer:

Explanation:

Let the speed of the goods train be $x$ kmph

Distance covered by goods train in 10 hours = Distance covered by express train in 4 hours

$10x=4\times 90$ or $x=36$.

So, speed of goods train = 36 kmph.

If a man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, If he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival the train. Find the distance covered by him to reach the station.

Answer:

Explanation:

Let the required distance be $x$ km.

Difference in the times taken at two speeds = 12 min $=\frac{1}{5}$ hr

$\left(\frac{x}{5}-\frac{x}{6}\right)$ $=\frac{1}{5}$ $\Leftrightarrow 6x-5x=6$ $\Leftrightarrow x=6$

Hence, the required distance is 6 km.

• Time and Distance - General Questions
• Time and Distance - Data Sufficiency 1