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Distance between two cars at finish

CAT 2018 Slot 2 · Quantitative Ability · Medium · Speed, Distance & Time

This is a medium Quantitative Ability question from the CAT 2018 Slot 2 paper. It tests Speed, Distance & Time. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

5

Explanation

Time taken by Car 1 to travel first 20 km20\text{ km} (at 100 kmph100\text{ kmph}) =20100=0.2 hours=12 minutes= \frac{20}{100} = 0.2\text{ hours} = 12\text{ minutes}. So Car 2 starts 0.2 hours0.2\text{ hours} after Car 1.

Total time taken by Car 1 to reach B (150 km150\text{ km}):

  • First 50 km50\text{ km} at 100 kmph  ⟹  0.5 hrs100\text{ kmph} \implies 0.5\text{ hrs}
  • Next 50 km50\text{ km} at 50 kmph  ⟹  1.0 hrs50\text{ kmph} \implies 1.0\text{ hrs}
  • Last 50 km50\text{ km} at 25 kmph  ⟹  2.0 hrs25\text{ kmph} \implies 2.0\text{ hrs} Total time for Car 1 =3.5 hours= 3.5\text{ hours}.

When Car 1 reaches B, Car 2 has been travelling for 3.5−0.2=3.3 hours3.5 - 0.2 = 3.3\text{ hours}. In 3.3 hours3.3\text{ hours}, Car 2 covers:

  • First 50 km50\text{ km} in 0.5 hrs0.5\text{ hrs}
  • Next 50 km50\text{ km} in 1.0 hrs1.0\text{ hrs}
  • Remaining time =3.3−1.5=1.8 hrs= 3.3 - 1.5 = 1.8\text{ hrs} at speed 25 kmph25\text{ kmph}. Distance covered in last leg =1.8×25=45 km= 1.8 \times 25 = 45\text{ km}.

Total distance covered by Car 2 =50+50+45=145 km= 50 + 50 + 45 = 145\text{ km}. Distance between Car 2 and B =150−145=5 km= 150 - 145 = 5\text{ km}.

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