AFCAT Model Paper 4

Given: The ratio of speed of trains = 5 : 7 Both trains take 4 seconds to cross the telegraph post Formula Used: Distance = Speed × Time Calculation: Let the speed of Train $1 = S_1 = 5 a \mathrm{m}/\mathrm{s}$. Let the length of Train $1 = L_1$ Let the speed of Train $2 = S_2 = 7 a \mathrm{m}/\mathrm{s}$. Let the length of Train $2 = L_2$ Time taken for the train to cross the telegraph post = (Length of the train)/(Speed of the train) For Train 1, $4 = \frac{L_1}{5a}$ ⇒ $L_1 = 20 a$ For Train 2, $4 = \frac{L_2}{7a}$ ⇒ $L_2 = 28 a$ Time taken by both the trains to cross each other completely =(Sum of length of the trains)/(sum of speed of the trains) {∵ Trains are crossing each other, they travel in opposite directions} ⇒ Time taken $= \frac{20a + 28a}{5a + 7a}$ ⇒ Time taken $= \frac{48a}{12a}$ ∴ Time taken = 4 sec