Aptitude Discussion

Q. |
A good train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in 60 sec. Whereas a passenger on the passenger train marks that he crosses the goods train in 40 sec. If the speeds of the trains be in the ratio 1:2. Find the ratio of their lengths. |

✖ A. |
$3 : 1$ |

✔ B. |
$2:1$ |

✖ C. |
$3 : 2$ |

✖ D. |
$4 : 3$ |

**Solution:**

Option(**B**) is correct

Let the speeds of the two trains be $s$ and 2s m/s respectively.

Also, suppose that the lengths of the two trains are $P$ and $Q$ metres respectively.

Then,

\(\dfrac{P+Q}{2s-s}=60\)------(1)

and

\(\dfrac{P}{2s-s}=40\)------(2)

On dividing these two equation we get:

\(\dfrac{P+Q}{P}=\dfrac{60}{40}\)

$P:Q$ = **2 : 1**

**Raj Singh**

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**Vaibhav Varish**

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#Akshay solution is right ..think it as passenger starts a clock when first bogie of goods train arrives and stops at last bogie .So it measures other(goods--P)train length in 2nd equation.while in case of goods train driver its starts its clock on first passenger bogie and stops on last bogie so .passenger train ultimately travels whole-(P+Q) as in first equation.

**Shikha Bharti**

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Not able to solve. Pls help me akshay. #shikha

**Akshay**

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I think this solution is wrong as the person in passenger train also moving with 2s and as per the question "Whereas a passenger on the passenger train marks that he crosses the goods train in 40 sec." so it implies length of train according to him should be the length of goods train nor the passenger train + goods train .please check its option should be (C)3:2

Not able to solve. Pls help me akshay..

Yes for passenger it should be Q. But for driver it is P+Q as he seen the train coming from behind means when train just started to overtake. I e when Ist bogie of passengers train come near to last bogie of good train.

I think Akshay is right, answer should be (C) 3:2.

@Shikha : both the trains are moving in same direction so relative speed is considered i.e. subtraction of both speeds 2s-s. If both train had been moving in opposite direction then relative speed is addition of duo.

Now assume, goods train is standing still and driver watches that passenger train passes him in P/2s=60 secs. But, both the trains are moving then the equation changes to P/(2s-s)=60 secs. Similarly, for the passenger in passenger train Q/(2s-s)=40 secs.