Quantitative Aptitude on Times and Distance
Q21. A car completes a certain journey in 8 hours. It coveres half of the distance at 30 km/hr and the rest at 50 km/hr. The length of the journey is
(a) 250 km
(b) 265 km
(c) 280 km
(d) 300 km
Answer: (d) 300 km
Let, the length of the journey be x Km
| A/Q | x | X | 1 | + | x | X | 1 | = 8 |
| 2 | 30 | 2 | 50 |
| ⇒ | x | + | x | = 8 |
| 60 | 100 |
| ⇒ | 5x + 3x | = 8 |
| 300 |
⇒ 8x = 8 X 300
⇒ x = 300 km
Q22. A man walking at 3 km/hr crosses a square field diagonally in 4 minutes. The area of the field is
(a) 15000 m2
(b) 17000 m2
(c) 20000 m2
(d) 25000 m2
Answer: (c) 20000 m2
| Speed = 3 km/hr = | 3 km | = | 3000 m | = 50 m/minute |
| 1 hr | 60 minute |
∴ Distance covered in 4 minutes = 4 X 50 meter = 200 meter
∴ Length of the diagonal = 200 meters
∴ Area = ½ X diagonal2 = ½ X 20002 = ½ X 200 X 200 = 20000 m2
Q23. Convert 60 km/hr into m/sec
(a) 15½ m/sec
(b) 162/3 m/sec
(c) 16¼ m/sec
(d) 17¾ m/sec
Answer: (b) 162/3 m/sec
| Speed = 60 km/hr = | 60 km | = | 60 X 1000 m | = | 100 | m/sec = 164/6 m/sec = 162/3 m/sec |
| 1 hr | 60 X 60 sec | 6 |
Q24. Convert 20 m/sec into km/hr
(a) 55 km/hr
(b) 59 km/hr
(c) 63 km/hr
(d) 72 km/hr
Answer: (d) 72 km/hr
| Speed = | 20 m | = | 20/1000 km | = | 20 X 60 X 60 | km/hr = 72 km/hr |
| 1 sec | 1/60 X 60 hr | 1000 |
Q25. A man walks from his house to the railway station. If he walks at 6 km/h, he misses a train by 6 minutes. However, if he walks at 7 km/h, he reaches the station 4 minutes before the diparture of the train. Find the distance covered by him to reach the station.
(a) 7 km
(b) 9 km
(c) 10 km
(d) 12 km
Answer: (a) 7 km
Let, the required distance be x km
| Now | x | - | x | = | 6 + 4 | = | 10 |
| 6 | 7 | 60 | 60 |
| ⇒ | x | - | x | = | 1 |
| 6 | 7 | 6 |
| ⇒ | 7x - 6x | = | 1 |
| 42 | 6 |
⇒ x = 1/6 X 42 = 7 km
Q26. A man covers a certain distance by walk at 6 km/hr and returns back to the starting point riding on scooter at 50 km/hr. Find his average speed of the whole journey.
(a) 32.48 km/h
(b) 49.12 km/h
(c) 54.54 km/h
(d) 59.65 km/h
Answer: (c) 54.54 km/h
| Average Speed = | 2xy | Km/h = | 2 X 60 X 50 | Km/h |
| x + y | 60 + 50 |
| = | 2 X 60 X 50 | Km/h = | 600 | Km/h = 54.54 Km/h |
| 110 | 11 |
Q27. A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 km/h. This train catches up the goods train in 4 hours. Find the speed of the goods train.
(a) 29 km/h
(b) 32 km/h
(c) 36 km/h
(d) 41 km/h
Answer: (c) 36 km/h
Let, the speed of the goods train be x km/h
Distance covered by goods train in 10 hours = Distance covered by express train in 4 hours
⇒ 10x = 4 X 90
⇒ x = (4X90)/10 = 36 km/h
Q28. The ratio between the speeds of two trains is 4:6. If the first train runs 280 km in 4 hours, the speed of the second train is
(a) 85 km/h
(b) 89 km/h
(c) 98 km/h
(d) 105 km/h
Answer: (d) 105 km/h
Let, the speed of the second train be 6x km/h
∴ the speed of the first train be 4x km/h
| A/Q 4x = | 280 |
| 4 |
⇒ 4x = 70
⇒ x = 70/4 = 35/2
∴ Speed of the second train = 6 X 35/2 = 3 X 35 = 105 km/h
Q29. Excluding stoppages, the speed of a bus is 50 km/h and including stoppages, it is 40 km/h. For how many minutes does the bus stop per hour ?
(a) 12 min
(b) 16 min
(c) 18 min
(d) 21 min
Answer: (a) 12 min
Due to stoppages, it covers (50 - 40) i.e 10 km less per hour
∴ Time taken to cover 10 km = (10/50 X 60) min = 12 min
Q30. X and Y are two stations 600 km apart. A train starts from X and moves towards Y at a speed 30 km/h. Another train starts from Y at the same time and moves towards X at 40 km/h. How far from X will they cross each other ?
(a) 257.11 km
(b) 266.22 km
(c) 312.35 km
(d) 323.39 km
Answer: (a) 257.11 km
Suppose, they meet x km from X
| Now | x | = | 600 - x |
| 30 | 40 |
| ⇒ | x | = | 600 - x |
| 3 | 4 |
⇒ 4x = 1800 - 3x
⇒ 7x = 1800
⇒ x = 257.11 Km
Practice Test Exam