Question

Points A and B are

150 km

apart. Cars

1

and

2

travel from A to B, but car

2

starts from A when car

1

is already

20 km

away from A. Each car travels at a speed of

100 kmph

for the first

50 km

, at

50 kmph

for the next

50 km

, and at

25 kmph

for the last

50 km

. The distance, in km, between car

2

and B when car

1

reaches B is _____.

Accepted Answer

According to the question,

Distance between A and B $= 150 km$

$T i m e = \frac{D i s \tan c e}{S p e e d}$

Cars $50 km$ and $2$ travel from A to B, but car $25 kmph$ starts from A when car $1$ is already $50 km$ away from A. Each car travels at a speed of $2$ for the first $50 km$ , at $50 kmph$ for the next $50 km$ , and at $25 kmph$ for the last $50 km$ .

Time taken by either of the cars to cover first $50 k m$ at $100 k m p h$ speed:

$T i m e = \frac{50}{100} = 1.5$ hours

Time taken by either of the cars to cover second $50 k m$ at $50 k m p h$ speed:

$T i m e = \frac{50}{50} = 1$ hours

Time taken either of the cars to cover last $25 k m$ at $25 k m p h$ speed:

$T i m e = \frac{50}{25} = 2$ hours

Total time taken by either of the cars $= 1.5 + 1 + 2 = 3.5$ hours

$3.5$ hours $= 3$ hours $30$ minutes

As per question, when car $2$ starts, car $1$ has already covered $20 k m$ distance.

So, time taken by car $2$ to reach $B$ after car $1$ starts:

Total time $-$ Time required to travel first $20 k m = 3 h o u r 30 m i n - \frac{(20 \times 60)}{100} m i n = 3 h o u r s 30 m i n - 12 m i n = 3 h o u r s 18 m i n$

Thus, we see that car $2$ lags behind by $12$ minutes.

The distance that remains to be covered by car $2$ during these $12$ minutes in the last leg of the travel with speed of $25 k m p h$ is:

Distance $= \frac{25}{60} \times 12 = 5 k m$

Thus, the distance between car $2$ and B when car $1$ reaches B is $5 k m$ .

Hence, the correct answer is $5 k m$ .

Nishit K Sinha Solutions for Chapter: Arithmetic, Exercise 7: Practice Exercises

Nishit K Sinha Quantitative Aptitude Solutions for Exercise - Nishit K Sinha Solutions for Chapter: Arithmetic, Exercise 7: Practice Exercises

Questions from Nishit K Sinha Solutions for Chapter: Arithmetic, Exercise 7: Practice Exercises with Hints & Solutions

Learn and Prepare for any exam you want !