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.

Walking at $\frac{5}{6}$ of its usual speed, a train is 10 minutes too late. Find its usual time to cover the journey.

Answer:

Explanation:

New speed $=\frac{5}{6}$ of the usual speed

New time taken $=\frac{6}{5}$ of the usual time

so, $\frac{6}{5}$ of the usual time - usual time = 10 mn.

$\Rightarrow$ $\frac{1}{5}$ of the usual time = 10 min $\Rightarrow$ usual time = 50 min.

An aeroplane flies along the four sides of a square field at the speeds of 200, 400, 600 and 800 km/hr. Find the average speed of the plane around the field.

Answer:

Explanation:

Let each side of the square field be $x$ km and let the average speed of the plane around the field be $y$ km/hr.

Then, $\frac{x}{200}+\frac{x}{400}+\frac{x}{600}+\frac{x}{800}$ $=\frac{4x}{y}$

$\Leftrightarrow y=\left(\frac{2400\times4}{25}\right)$ $=384$

Average speed = 384 km/hr.

A man travelled from the village to the post-office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village.

Answer:

Explanation:

Average speed $=\frac{2xy}{x+y}$ km/hr $=\frac{2\times25\times4}{25+4}$ km/hr $=\frac{200}{29}$ km/hr

Distance travelled in 5 hours 48 minutes i.e., $5\frac{4}{5}$ hrs $=\left(\frac{200}{29}\times\frac{29}{5}\right)$ km $=40$km

Distance of the post-office from the village $=\frac{40}{20}$ = 20km.

Saji can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance.

Answer:

Explanation:

Let the total distance be $x$ km. Then,

$\frac{\frac{2}{3}x}{4}+\frac{\frac{1}{3}x}{5}$ $=\frac{7}{5}$ $\Leftrightarrow x=6$

Total distance = 6 km.

While covering a distance of 24 km, a man noticed that after walking for 1 hour and 40 minutes, the distance covered by him was $\frac{5}{7}$ of the remaining distance. What was his speed in metres per second ?

Answer:

Explanation:

Let the speed be $x$ km/hr.

Then, distance covered in 1 hr. 40 min. i.e. $1\frac{2}{3}$ hrs $=\frac{5x}{3}$ km

Remaining distance $=\left(24-\frac{5x}{3}\right)$ km

$\frac{5x}{3}=\frac{5}{7}\left(24-\frac{5x}{3}\right)$

$\Leftrightarrow\frac{5x}{3}=\frac{5}{7}\left(\frac{72-5x}{3}\right)$

$\Leftrightarrow 7x=72-5x$

Hence, speed = 6 km/hr $=\left(6\times\frac{5}{18}\right)$ m/sec

$=\frac{5}{3}$ m/sec $=1\frac{2}{3}$ m/sec.

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