CAT 2018 Question Paper Shift 1 Solved Paper

Train T starts at 3 PM and train S starts at 4 PM. Let the speed of train $T$ be $t$. $\Rightarrow$ Speed of train $S = 0.75 t$ When the trains meet, train $t$ would have traveled for one more hour than train $S$. Let us assume that the 2 trains meet $x$ hours after 3 PM. Trains S would have traveled for $x-1$ hours. Distance traveled by train $T = xt$ Distance traveled by train $S = (x-1) \cdot 0.75 t = 0.75 xt - 0.75 t$ We know that train T has traveled three fifths of the distance. Therefore, train S should have traveled two-fifths the distance between the 2 cities. $\Rightarrow \frac{x t}{0.75 x t - 0.75 t} = \frac{3}{2}$ $2 xt = 2.25 xt - 2.25 t$ $0.25 x = 2.25$ $x = 9$ hours. Train T takes 9 hours to cover three-fifths the distance. Therefore, to cover the entire distance, train T will take $9 \cdot \left(\frac{5}{3}\right) = 15$ hours. Therefore, 15 is the correct answer.train