CAT 2017 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Speed Time Distance Questions | Question 4

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Question 4 : Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance travelled by him is :

  1. 55 miles
  2. 60 miles
  3. 65 miles
  4. 70 miles

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Explanatory Answer

Method of solving this CAT Question from Speed Time Distance
CAT 2017 Question Paper Quants Slot 2 Speed Time Distance

Given that Arun drove from home to his hostel at 60 miles per hour . Let us consider this distance to be 2d,
Hence, the time taken for onward journey taken is \\frac{2d}{60}) .
While returning he drove half way i.e. d at a speed of 25 miles per hour hence the time taken is \\frac{d}{25}) and then took a bypass road for which the time taken is \\frac{d + 5}{50}) .
While returning the total time taken is \\frac{d}{25}) + \\frac{d + 5}{50}) .
His return journey took 30 minutes more than his onward journey,
⟹ \\frac{d}{30}) + \\frac{1}{2}) = \\frac{d}{25}) + \\frac{d}{50}) + \\frac{1}{10})
⟹ \\frac{d}{30}) + \\frac{1}{2}) = \\frac{2d}{50}) + \\frac{d}{50}) + \\frac{1}{10})
⟹ \\frac{d}{30}) + \\frac{1}{2}) = \\frac{3d}{50}) + \\frac{1}{10})
⟹ \\frac{1}{2}) - \\frac{1}{10}) = \\frac{3d}{50}) - \\frac{d}{30})
⟹ \\frac{5}{10}) - \\frac{1}{10}) = \\frac{3d}{50}) - \\frac{d}{30})
⟹ \\frac{2}{5}) = \\frac{9d - 5d}{150})
⟹ \\frac{2}{5}) = \\frac{4d}{150})
⟹ d =15 miles
We have to find the total distance travelled by him
. i.e. 2d + d + d + 5 = 4d + 5 = 4(15) + 5 = 65 miles

The question is "Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance travelled by him is :"

Hence, the answer is 65 miles

Choice C is the correct answer

 

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