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CAT 2018 Slot 2 — QA Question 2

Basics of TSD/ProportinalityEasy

Points A and B are 150 km apart. Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is already 20 km away from A. Each car travels at a speed of 100 kmph for the first 50 km, at 50 kmph for the next 50 km, and at 25 kmph for the last 50 km. The distance, in km, between car 2 and B when car 1 reaches B is

Answer & solution

Answer: 5

Solution

Easy

Both cars follow the identical speed profile over the same 150150 km route, so car 2 simply trails car 1 by a fixed time gap throughout. Find that time gap, then convert it into a distance using car 2's speed on its final leg.

1

Time gap between the cars. Car 2 starts when car 1 is 2020 km from A. In the first leg the speed is 100100 km/h, so the head-start in time is:

tgap=20100=0.2 h⇒ tgap=0.2×60=12 minutes\begin{aligned} &t_{\text{gap}} = \frac{20}{100} = 0.2\ \text{h}\\ &\Rightarrow\ t_{\text{gap}} = 0.2\times 60 = 12\ \text{minutes} \end{aligned}
2

The gap stays 1212 minutes. Since both cars use the same speeds on every leg, car 2 is always exactly 1212 minutes behind car 1. So when car 1 reaches B, car 2 is 1212 minutes of travel short of B.

3

Convert the 1212 minutes to distance. Near B the cars are on the last 5050 km leg at 2525 km/h.

d=25×1260(speed × time on final leg)⇒ d=5 km\begin{aligned} &d = 25\times \frac{12}{60} \quad\text{(speed }\times\text{ time on final leg)}\\ &\Rightarrow\ d = 5\ \text{km} \end{aligned}
Distance of car 2 from B=5 km\text{Distance of car 2 from B} = 5\ \text{km}
CAT 2018 Slot 2 QA Q2: Points A and B are 150 km apart. Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is alread — Solution | TheCATExam