Question 17

Only a single rail track exists between stations A and B on a railway line. One hour after the northbound super fast train N leaves station A for station B, a south-bound passenger train S reaches station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day, N leaves for B from A, 20 min behind the normal schedule. In order to maintain the schedule, both N and S increased their speeds. If the super fast train doubles its speed, what should be the ratio (approximately) of the speeds of passenger train to that of the super fast train so that the passenger train S reaches exactly at the scheduled time at A on that day?

Solution

Let the speed of an express train be 4x, normal train be 2x and passenger train be x.

Let the distance between the 2 stations be D.

Since there is only 1 railway track, train N must reach station B before train S leaves.

Therefore, D/4x + D/x = 60

5D/4x = 60

D/x = 48

Train N leaves 20 minutes late. Therefore, the 2 trains must have covered the distance within 40 minutes on this particular day.

Train N doubles its speed. Therefore, speed of train N will be 8x. Let the new speed of the passenger train be y.

D/8x + D/y = 40

48/8 + D/y = 40

D/y = 34.

Speed of super fast train = D/8x = 6

Speed of passenger train = D/y = 34

Ratio of the speeds = 6/34 = 3/17.

The ratio is approximately equal to 1:6. Therefore, option D is the right answer.

Create a FREE account and get:

- All Quant CAT Formulas and shortcuts PDF
**33+**CAT previous papers with video solutions PDF- Topic-wise Previous year CAT Solved Questions for Free

CAT Linear Equations Questions
CAT Inequalities Questions
CAT Quadratic Equations Questions
CAT Averages, Ratios & Proportions Questions
CAT Profit & Loss Questions
CAT Number Systems Questions
CAT Time, Distance & Work Questions
CAT Geometry Questions
CAT Progressions & Series Questions
CAT Probability Combinatorics Questions
CAT Venn Diagrams Questions
CAT Data Sufficiency Questions
CAT Logarithms, Surds & Indices Questions
CAT Functions, Graphs & Statistics Questions
CAT Miscellaneous Questions

CAT DI Basics Questions
CAT DI Charts Questions
CAT Data Interpretation Questions
CAT DI Data Change Over Period Questions
CAT Tables With Missing Values Questions
CAT DI Venn Diagrams Questions
CAT DI Special Charts Questions
CAT DI Maxima & Minima Questions
CAT Quant-Based DI Questions
CAT DI Connected Sets Questions
CAT DI Miscellaneous Questions
CAT LR Arrangement Questions
CAT LR Selections With Conditions Questions
CAT LR Coins & Weights Questions
CAT LR Truth & Lie Questions
CAT LR Puzzles Questions
CAT LR Scheduling Questions
CAT LR Games & Tournaments Questions
CAT 2D & 3-D LR Questions
CAT Quant-Based LR Questions
CAT LR Miscellaneous Questions