Question

Time taken by a train, when travelling at 72 kmph, to cross a platform is 6 times the time taken by it, when travelling at 126 kmph, to cross an electric pole. What is the respective ratio of the length of the platform and that of the train ?

Answer 1

Hi,

Answer:

Length of platform : Length of train = 17 : 7

Step-by-step explanation:

Let the length of the train be “L1” and length of the platform be “L2”.

Case 1: when the train crosses a platform

Speed of the train, S1 = 72 km/hr = (72*5)/18 = 20 m/s

Time taken by the train to cross the platform be “T1”.

Therefore,  

Distance traveled by train = L1+L2  

And,  

Time taken, T1 = (L1+L2)/S1 = $\frac{L1+L2}{20}$ seconds ….. (i)

Case 2: when train crosses an electric pole

Speed of the train, S2 = 126 km/hr =(126*5)/18= 35 m/s

Time taken by the train to cross the pole be “T2”.

Distance traveled by train = Length of the train, L1 = S2 * T2

∴ T2 = L1 / S2 = $\frac{L1}{35}$ seconds…. (ii)

We are given that  

T1 = 6 * T2

Putting the values from (i) & (ii), we get

(L1+L2)/20 = 6 * (L1 / 35)

Or, (L1+L2)/20 = 6* (L1 / 35)

Or, 35L1 + 35L2 = 120L1

Or, 35 L2 = 85 L1

Or, $\frac{L2}{L1}$ = $\frac{85}{35}$

or, $\frac{L2}{L1}$ = $\frac{17}{7}$

Hence, the respective ratio of the length of the platform and that of the train is 17:7.

Hope it helps!!!!!