Aptitude Discussion

Q. |
A thief steals a car and drives it at 15 km/hr. The theft has been discovered after one hour and the owner of the car sets off in another car at 25 km/hr. When will the owner overtake the thief from the starting point? |

✖ A. |
1 hr |

✔ B. |
1.5 hr |

✖ C. |
2 hr |

✖ D. |
2.5 hr |

**Solution:**

Option(**B**) is correct

Distance covered by the thief in one hour = 15 km

Now this distance is to be covered by the relative speed of $(25−15)=10$ km/hr

Hence, time required to cover this distance at a speed of 10 km/hr:

\(=\dfrac{10}{15}\)

= **1.5 hr**

**Ratishchandran Nair**

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**Manohar Tangi**

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initially, distance between owner and thief is 15 km.(thief speed=15kmph)

owner gains 10km in one hour.(25-15)km

so total 15 km gained by owner is

=15/10

=1.5hr.

**NerdBird**

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From the moment of discovery, it should take 1.5 hours. However, from the starting point to the point of discovery, an hour has already passed, so shouldn't it 1+1.5= 2.5 hours? If I'm wrong, please do explain where.

If you solve it using the normal method you may consider this. the beauty of relative speed method is that it eliminates such extra calculation. It is already considered in the initial 1 hr time.

**Lakshya**

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it should be 15/10 as total distance is 10 km that is required to be chased and total speed(relative , as both are driving in the same direction ) is

10km/hr .

**Amaresh Chauhan**

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If the thief has been discovered in one hour, how is it possible that the owner took 1.5 hours to overtake the thief.......?

Or question description may not be appropriate...!!!

It seems perfectly fine to me. After 1 hour of the theft, the owner comes to know about it and catches the thief in the next 1.5 hr (total 2.5 hrs right after the theft).

What's not appropriate in that?

**Amaresh Chauhan**

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If the thief has been discovered in one hour, how is it possible that the owner overtook the thief in1.5 hours to overtake.......?

Or question description may not be appropriate...!!!

**Suhail Ahmed**

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Or simply follow this formula:

$=\dfrac{s1*T}{s2-s1}$

If time is given as for example, 8:00 PM to 10:00 PM, then $T=2$

Relative speed is 10km/hr

Owner traves at a speed of 25km in 60 min.

To cover 10 km, it takes 24 min by the owner.

Already 1 hour is lapsed. Therefore, total time will be 1h24min or ~1.5 hours