Question

Two trains running in opposite direction cross a tree in 60 seconds and 75 seconds respectively. Find the ratio of the length of the train if they cross each other in 70 seconds.
1. 5 ∶ 2
2. 2 ∶ 5
3. 3 ∶ 5
4. 5 ∶ 3
5.

Answer 1

Correct Answer - Option 2 : 2 ∶ 5

Given:

Two trains cross each other in 70 seconds

Two trains cross a tree in 60 seconds and 75 seconds respectively

Formula used:

L_Train = S_Train × T

Where, LTrain is Length of the train, STrain is Speed of the train and T is time taken

Calculations: 

Let the length of the train₁ and the train₂ be L₁ and L₂ respectively

Let the spped of the train1 and the train2 be S1 and S2 respectively

According to the question, we have

The length of train L1 is 

⇒ L1 = S₁ × 60

⇒ S₁ = L1/60

The length of train L₂ is 

⇒ L₂ = S₂ × 75

⇒ S₂ = L₂/75

Time taken by the train to cross each other

⇒ T = (L1 + L₂)/(S₁ + S₂)

⇒ 70 = (L1 + L2)/{(L₁/60) + (L2/75)}

⇒ 70 = (L1 + L2)/{(5L₁ + 4L2)/300}

⇒ 70(5L1 + 4L2) = 300(L₁ + L2)

⇒ 350L1 + 280L2 = 300L₁ + 300L2

⇒ 350L1 - 300L₁ = 300L2 - 280L2

⇒ 50L1 = 20L2

⇒ L1/L2 = 20/50

⇒ L1 : L2 = 2 : 5 

∴ The ratio of length of the train1 and the train2 be L1 and L2 is 2 : 5.