CAT 2025 Slot 3 · Quant · Question 16

CAT 2025 Slot 3 previous year question on Time Speed and Distance, with the answer and a step-by-step solution.

Time Speed and DistanceArithmeticType in the answer (TITA)Medium

Ankita walks from A to C through B, and runs back through the same route at a speed that is 40% more than her walking speed. She takes exactly 3 hours 30 minutes to walk from B to C as well as to run from B to A. The total time, in minutes, she would take to walk from A to B and run from B to C, is

Answer & solution

Answer: 444

Let her walking speed be w, so her running speed is 1.4w.

Both given journeys take 3 hours 30 minutes, which is 210 minutes.

Walking from B to C at speed w for 3.5 hours gives BC=3.5w.

Running from B to A at speed 1.4w for 3.5 hours gives AB=1.4w\times 3.5=4.9w.

Walking from A to B takes \frac{4.9w}{w}=4.9 hours, which is 294 minutes.

Running from B to C takes \frac{3.5w}{1.4w}=2.5 hours, which is 150 minutes.

The total is 294+150=444 minutes.

Shortcut. Each leg asked for covers the same ground as a given leg, but at the other speed. So walking A to B takes 210\times 1.4=294 minutes, and running B to C takes \frac{210}{1.4}=150 minutes. The distances and the speed w never need naming at all.

CAT 2025 Slot 3 · Quant · Question 16

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