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Question 1 of 5
1. Question
A train travels 25% faster than a car. Both start together to cover 80 km. The train halts at stations for 12 minutes, yet they reach together. The speed of the car is:
Correct
Answer – C
Solution:Given that,
Train is 25% faster than car.
Let car speed be v kmph ⇒ train speed = 1.25v = 5v/4 kmph.
Now,
Car time = 80/v.
Train running time = 80/(5v/4) = 64/v.
Halt time = 12 minutes = 12/60 = 1/5 hour.So,
80/v = 64/v + 1/5 ⇒ 16/v = 1/5 ⇒ v = 16 × 5 = 80 kmph.
Hence option (c) is correct
Incorrect
Answer – C
Solution:Given that,
Train is 25% faster than car.
Let car speed be v kmph ⇒ train speed = 1.25v = 5v/4 kmph.
Now,
Car time = 80/v.
Train running time = 80/(5v/4) = 64/v.
Halt time = 12 minutes = 12/60 = 1/5 hour.So,
80/v = 64/v + 1/5 ⇒ 16/v = 1/5 ⇒ v = 16 × 5 = 80 kmph.
Hence option (c) is correct
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Question 2 of 5
2. Question
Seema plans to reach office by 5 P.M. if she drives at 20 kmph; she would reach by 3 P.M. if she drives at 30 kmph. At what speed must she drive to reach by 4 P.M.?
Correct
Answer – B
Solution:Given that,
At 20 kmph arrival is 5 P.M., at 30 kmph arrival is 3 P.M. (2 hours earlier).
Let the distance be D.
Now,
D/20 − D/30 = 2
D(1/20 − 1/30) = 2 ⇒ D(1/60) = 2 ⇒ D = 120 kmAt 20 kmph, time = 120/20 = 6 hours (5 P.M.).
To reach at 4 P.M. (1 hour earlier), required time = 5 hours.Required speed = 120 / 5 = 24 kmph
Hence option (b) is correct
Incorrect
Answer – B
Solution:Given that,
At 20 kmph arrival is 5 P.M., at 30 kmph arrival is 3 P.M. (2 hours earlier).
Let the distance be D.
Now,
D/20 − D/30 = 2
D(1/20 − 1/30) = 2 ⇒ D(1/60) = 2 ⇒ D = 120 kmAt 20 kmph, time = 120/20 = 6 hours (5 P.M.).
To reach at 4 P.M. (1 hour earlier), required time = 5 hours.Required speed = 120 / 5 = 24 kmph
Hence option (b) is correct
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Question 3 of 5
3. Question
A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 2 km/h and Y walks with a uniform speed of 1 km/h in the first hour, 1.25 km/h in the second hour, 1.5 km/h in the third hour, 1.75 km/h in the fourth hour and 2 km/h in the fifth hour and so on.
Which of the following is/are correct?
- They take 5 hours to meet.
- They meet midway between A and B.
Correct
Answer – D
Solution:Given that,
Total distance between A and B = 15 km
X walks with a uniform speed = 2 km/h
Y’s hourly speeds = 1, 1.25, 1.5, 1.75, 2, …
Now,
After 4 hours:
X covers = 2 × 4 = 8 km
Y covers = 1 + 1.25 + 1.5 + 1.75 = 5.5 km
Total = 13.5 km; remaining = 15 − 13.5 = 1.5 kmIn the 5th hour, speeds are X = 2 km/h and Y = 2 km/h ⇒ combined = 4 km/h.
Time to finish remaining 1.5 km = 1.5/4 = 0.375 hour = 22.5 minutes.Therefore, they meet in 4 hours 22.5 minutes (not 5 hours), and distances at meet:
X total = 8 + (2 × 0.375) = 8.75 km; Y total = 5.5 + (2 × 0.375) = 6.25 km (not midpoint 7.5 km).- They take 5 hours to meet. Hence statement 1 is incorrect
- They meet midway between A and B. Hence statement 2 is incorrect
Hence option (d) is correct
Incorrect
Answer – D
Solution:Given that,
Total distance between A and B = 15 km
X walks with a uniform speed = 2 km/h
Y’s hourly speeds = 1, 1.25, 1.5, 1.75, 2, …
Now,
After 4 hours:
X covers = 2 × 4 = 8 km
Y covers = 1 + 1.25 + 1.5 + 1.75 = 5.5 km
Total = 13.5 km; remaining = 15 − 13.5 = 1.5 kmIn the 5th hour, speeds are X = 2 km/h and Y = 2 km/h ⇒ combined = 4 km/h.
Time to finish remaining 1.5 km = 1.5/4 = 0.375 hour = 22.5 minutes.Therefore, they meet in 4 hours 22.5 minutes (not 5 hours), and distances at meet:
X total = 8 + (2 × 0.375) = 8.75 km; Y total = 5.5 + (2 × 0.375) = 6.25 km (not midpoint 7.5 km).- They take 5 hours to meet. Hence statement 1 is incorrect
- They meet midway between A and B. Hence statement 2 is incorrect
Hence option (d) is correct
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Question 4 of 5
4. Question
Two cars start towards each other from two places A and B which are at a distance of 150 km. They start at the same time 06:40 am. If the speeds of the cars are 40 km/h and 35 km/h respectively, they will meet each other at:
Correct
Answer – B
Solution:Given that,
Two cars start towards each other from A and B, 150 km apart.
They start at the same time 06:40 am.
The speeds of the cars are 40 km/h and 35 km/h respectively.
Now,
Relative speed = 40 + 35 = 75 km/hr
Distance = 150 km
Time taken = 150/75 = 2 hrs
06:40 am + 2 hours = 08:40 am
Hence option (b) is correct
Incorrect
Answer – B
Solution:Given that,
Two cars start towards each other from A and B, 150 km apart.
They start at the same time 06:40 am.
The speeds of the cars are 40 km/h and 35 km/h respectively.
Now,
Relative speed = 40 + 35 = 75 km/hr
Distance = 150 km
Time taken = 150/75 = 2 hrs
06:40 am + 2 hours = 08:40 am
Hence option (b) is correct
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Question 5 of 5
5. Question
A motorboat’s speed in still water is 15 km/h. It goes from P to Q and back. The round trip takes 12 hours, and the upstream journey takes 2 hours longer than the downstream journey. What is the speed of the stream?
Correct
Answer – B
Solution:
Given that,
Still-water speed = 15 km/h; upstream time = (downstream time) + 2 h; total = 12 h.
Now,
Let downstream time = t hours ⇒ upstream time = t + 2; so 2t + 2 = 12 ⇒ t = 5, upstream = 7.
Let stream speed = u. For one-way distance D:
D = (15 + u)×5 and also D = (15 − u)×7
(15 + u)×5 = (15 − u)×7 ⇒ 75 + 5u = 105 − 7u ⇒ 12u = 30 ⇒ u = 2.5 km/h
Hence option (b) is correct
Incorrect
Answer – B
Solution:
Given that,
Still-water speed = 15 km/h; upstream time = (downstream time) + 2 h; total = 12 h.
Now,
Let downstream time = t hours ⇒ upstream time = t + 2; so 2t + 2 = 12 ⇒ t = 5, upstream = 7.
Let stream speed = u. For one-way distance D:
D = (15 + u)×5 and also D = (15 − u)×7
(15 + u)×5 = (15 − u)×7 ⇒ 75 + 5u = 105 − 7u ⇒ 12u = 30 ⇒ u = 2.5 km/h
Hence option (b) is correct
