Dear Reader, Below are three practice relative speed problems. These are actually simple but could be lengthy consuming time.

**Question 1**

Two persons – Srikanth and Kashyap start at –6 am on 19th February 2012 from two places – Coimbatore and Hyderabad ( 900 km away at ) — each going towards the other end in two cars. Rupashri starts from Coimbatore at 7 am on the same day from Coimbatore towards Hyderabad. Srikanth, Rupashri and Kashyap travel at 40 km/hour, 60 km/hour and 50 km/hour respectively. Which pair will meet on the way – Srikanth –Kashyap or Kashyap-Rupashri or Srikanth-Rupashri.

a) Srikanth-Kashyap b) Srikanth-Rupashri c) Kashyap-Rupashri d) none of these.

**Answer : **b) Srikanth –Rupashri.

Solution :

**Case I :** Consider Srikanth and Kashyap

Distance between Coimbatore and Hyderabad – 900 km

Srikanth and Kashyap start at 6 am and their speeds are respectively 40 km/hour and 50 km/hour. So relative speed is 40 + 50 = 90 km. Hence they will meet after [distance between them/relative speed] = 900/90 = 10 hours from 6 am i.e 4 pm

**Case II:** Consider Rupashri and Kashyap

Rupashri starts at 7 am from Coimbatore – speed 60 km/hour. But since Kashyap had started at 6 am (1 hour earlier at 50Km/hr) he would have travelled 50 km by 7am. Distance between them = 900 – 50 =850 km. Relative speed = 60 + 50 = 110.

Rupashri and Kashyap will meet after [distance between them/relative speed] = 850/110 = 7 and 8/11 hours.

**Case III:** Consider Rupashri and Srikanth

On the other hand When Rupashri starts – 7 AM Srikanth would have travelled 40 km only (as Srikanth would had started at 6 am travelling at 40 Km/hr).

The speed of Rupashri and Srikanth = 60 and 40 km/hour. Relative speed of Rupashri with respect to Srikanth = 60 – 40 = 20 km per hour (we are subtracting the speeds in relative speed calculation as they are both travelling in same direction) and hence Rupashri will cross/meet Srikanth after [distance between them/relative speed] = 40/20 = 2 hours i.e. at 9 am.

**Inference :** Considering all discussed cases above, Srikanth-Rupashri will meet first at 9 am.

**Question 2**

The distance between Chennai and other cities is given below:

Agartala | 3356 | Gurgaon | 2088 | Panaji | 923 |

Agra | 1892 | Guwahati | 2718 | Paradwip | 1359 |

Ahmedabad | 1800 | Gwalior | 1768 | Pathankot | 2570 |

Aizawl | 3281 | Haldia | 1660 | Patna | 2022 |

Ajmer | 1978 | Hassan | 518 | Pondicherry | 165 |

Priya starts from Chennai at 8 AM, 20th February 2012 towards Ahmedabad. Shriya starts from Ahmedabad on the same day at 9 AM towards Chennai. Ramya starts from Chennai at 10 AM on the same day towards Ahmedabad. Which pair will meet on the way – Priya – Shriya or Ramya – Priya or Ramya – Shriya? Assume Priya travelled at 100 km/hour, Ramya travelled at 110 km/hour and Shriya travelled at 90 km/hour.

a) Priya-Shriya

b) Ramya – Priya

c) Ramya – Shriya

d) None of these.

**Answer : **a) Priya- Shriya

Solution :

In these types of problems careful analysis of information and appropriate understanding is very important. It is equally important to learn to identify relevant and irrelevant information in the data provided and discard the unwanted information. For example in this question distances between Chennai to other places except that of Ahmedabad is not required (unwarranted ) and can be safely ignored.

**Case I**

Priya starts at 8 am – speed – 100 km/hour. Shriya starts from Ahmedabad at 9 am with a speed of 90 km/hour. Original distance between Chennai and Ahmedabad is 1800 Km. But since Shriya has started 1 hour late, Priya would had covered 100 Kms (travelling at 100 Km/hr) by 9 am. Therefore, at 9 am distance between Priya and Shriya is 1800 – 100 = 1700 km. Relative speed = 100 + 90 = 190 km/hour. They will meet at [Distance between them / Relative speed] = 1700/190 = 8 18/19 hours from 9 am i.e. around 5.57 pm.

**Case II**

Ramya starts from Chennai at 10 am at 110 km/hour. But since Shriya has started at 9 am, she would had covered 90 Km (travelling at 90 Km/hr). At 10 am distance between Ramya and Shriya = 1800 + 90 = 1890 km. Relative speed = 110 + 90 = 200 km/hour. They will meet at [Distance between them / Relative speed] =1890/200 hours = 9 and 9/20 hours after 10 am. And it will be around 7.27 pm.

**Case III**

At 10 am when Ramya starts Priya would have travelled 200 km (as Priya had started at 2 hours earlier i.e at 8 am, she would had covered 200 Km in 2 hours till 10 am when Ramya starts). At 10 am Distance between Ramya and Priya is 200km. Relative speed is 110-100 = 10 km/hour (we are subtracting the speeds for relative speed calculation as both are travelling in same direction) and they will meet at [Distance between them / Relative speed] = 200/10 = 20 hours . But we know that Priya would had covered the entire distance between Chennai and Ahmedabad in Distance between two cities / Priya’s Speed = 1800/100 = 18 hours. This means that Ramya will not be able to meet Priya before reaching Ahmedabad.

**Inference : **Considering all the above cases, Priya- Shriya will be meeting first.

**Question 3**

The chart showing the distance of different cities/towns from Madurai is given below:

City | Distance (Kms) | City | Distance (Kms) | City | Distance (Kms) |
---|---|---|---|---|---|

Agartala | 3800 | Guntur | 840 | Panaji | 1024 |

Agra | 2304 | Gurgaon | 2500 | Paradwip | 1803 |

Ahmedabad | 1938 | Guwahati | 3162 | Pathankot | 2982 |

Akola | 1507 | Hasan | 533 | Porbandar | 2332 |

Allahabad | 2100 | Hubli | 851 | Purulia | 2146 |

Ambala | 2698 | Hyderabad | 1000 | Raipur | 1773 |

Karthik travelled from Madurai to Gurgaon in his car with an average speed of 130 km/hour starting at 5 am. Jeeva travelled from Hyderabad towards Madurai in his car with an average speed of 60 km/hour starting at 10 am on the same day. Surya started at 10 am for Hyderabad from Madurai and he travelled at an average speed of 40 km/hour. Vijay started at 5 am from Gurgaon towards Madurai and he was travelling at 120 km/hour. Which pair will meet first and at what time

a) Vijay – Karthik at 1 pm

b) Surya – Jeeva at 5 pm

c) Karthik – Vijay at 3 pm

d) Jeeva – Surya at 8 pm

**Answer : **c) Karthik – Vijay at 3 pm

Solution :

Relative speed of Karthik & Vijay pair – 130 + 120 = 250 km/hour.

Since both Vijay and Karthik start at 5 am the distance between them at the start will be exactly the distance between Madurai and Gurgaon from the chart = 2500 km. They will meet at [Distance between them / Relative speed] = 2500/250 = 10 hours from 5 am = 3 pm

Relative speed of Surya & Jeeva = 40 + 60 = 100 km/hour

Since both Surya and Jeeva started at 10 am, distance between them at the start will be exactly the distance between Madurai and Hyderabad from the chart – 100 km. They will meet at [Distance between them / Relative speed] = 1000/100 = 10 hours from 10 am = 8 pm.

So the pair Karthik- Vijay will meet first at 3 pm.