Aptitude Discussion

Q. |
The distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km per hour. Find the average speed of train during the whole journey. |

✖ A. |
60.3 km/hr |

✖ B. |
35.0 km/hr |

✖ C. |
57.5 km/hr |

✔ D. |
67.2 km/hr |

**Solution:**

Option(**D**) is correct

$\text{Average Speed} = \left(\dfrac{2xy}{x+y}\right)$ km/hr

$=\left(\dfrac{2\times 84 \times 56}{84+56}\right)$

$=\left(\dfrac{2\times 84 \times 56}{140}\right)$

$= \textbf{67.2 km/hr}$

**Edit:** For explanation on the formula used, check comment by **Sravan Reddy.**

**Intelligent Freak**

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**Monk**

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Can someone elaborate this one?

That is the formula for calculating the average speed when the distance traveled is same with varying speed.

Suppose $d$ is the distance and $s_1$,$s_2$ are speeds. then average speed is total distance divided by total time

Total distance is $2d$ and total time is $\dfrac{d}{s_1}+\dfrac{d}{s_2} = d \times \left(\dfrac{1}{s_1}+\dfrac{1}{s_2}\right)$

$\text{Average speed} = \dfrac{2d}{\text{total time}$ which by simplifying you get the equation given in solution description.

It is very easy monk

2(84*56)/84+56=67.20

Another way of doing question in case one forget the formula

Total distance = 778*2 = 1556

Total time taken to travel from A to B = 778/84 = 9.26

Total time taken to travel from B to A = 778/56 = 13.89

Total time = 23.15

Avg speed = total distance/ total time

Avg speed = 1556/23.15

Ans = 67.25