Aptitude Discussion

Q. |
Rajesh travelled from city $A$ to city $B$ covering twice as much distance in the second part as he did in the first part of this journey. His speed during the second part was twice as that of the speed during the first part of the journey. What is his average speed of journey during the entire travel? |

✖ A. |
His average speed is the harmonic mean of the individual speeds for the two parts. |

✔ B. |
His average speed is the arithmetic mean of the individual speeds for the two parts. |

✖ C. |
His average speed is the geometric mean of the individual speeds for the two parts |

✖ D. |
Cannot be determined. |

**Solution:**

Option(**B**) is correct

The first part is $\dfrac{1}{3^{rd}}$ of the total distance and the second part is $\dfrac{2}{3^{rd}}$ of the total distance. He travels at $s$ km/hr speed during the first half and $2s$ km/hr speed during the second half.

If 3 km is the total distance, then 1 km was travelled at $s$ km/hr and 2 kms was travelled at $2s$ km/hr speed

\(\text{Average speed}=\dfrac{\text{Total Distance}}{\text{Total Time}}\)

\(=\dfrac{1+2}{1/s+2/{2s}}\)

\(=\dfrac{3}{2/s}\)

\(=\dfrac{3s}{2}\)

Now, Arithmetic mean of the speeds of the two parts is,

\(=\dfrac{2s+s}{2}\)

\(=s+\dfrac{s}{2}\)

\(=\dfrac{3s}{2}\)

Thus, his average speed is the arithmetic mean of the individual speeds for the two parts.

**Edit:** Thank you **Sonu** and **ankit** for the your inputs in the disscussion page. Question has been updated.

**Meth Dealer**

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You sure not under the impression of meth (on a lighter note off course)?

Because

**Sonu**

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Its saying thrice as much distance as it covered in first part. so it should be 1/3 and 1 not 2/3.

Thank you Sonu for pointing it out. Updated the question, now TWICE as muck distance is mentioned in the question.

**Ankit**

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how did you calculated that first part journey distance is 1/3 while that of 2 part is 2/3 as it is clearly stated in question that equal distance is travelled in both part

It was a typo. Corrected it. Thank you for pointing it out.

Its the avg of individual distances....not the avg of individual speeds