Maths Quiz

1. A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
A. 3.6
B. 7.2
C. 8.4
D. 10


2. An aeroplane covers a certain distance at a speed of 240 kmph in 5/3 hours. To cover the same distance in 1 hours, it must travel at a speed of:
A. 300 kmph
B. 360 kmph
C. 600 kmph
D. 720 kmph

3. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
A. 50 km
B. 56 km
C. 70 km
D. 80 km

4. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
A. 100 kmph
B. 110 kmph
C. 120 kmph
D. 130 kmph

5. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
A. 9
B. 10
C. 12
D. 20

6. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:
A. 1 hour
B. 2 hours
C. 3 hours
D. 4 hours

7. A man completes a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
A. 220 km
B. 224 km
C. 230 km
D. 234 km

8. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
A. 70 km/hr
B. 75 km/hr
C. 84 km/hr
D. 87.5 km/hr

9. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
A. 35.55 km/hr
B. 36 km/hr
C. 71.11 km/hr
D. 71 km/hr

 10. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
A. 5 kmph
B. 6 kmph
C. 6.25 kmph
D. 7.5 kmph


ANSWERS:
1. B
Explanation:
Speed = 600/(5*60) m/sec
   = 2 m/sec
   = 2 x 18/5 km/hr
   = 7.2 km/hr

2. D
Explanation:
Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr.
Required speed = (1200 x 3)/5km/hr = 720 km/hr.

3. A
Explanation:
Let the actual distance travelled be x km.
Then, x/10 = (x + 20)/14
 14x = 10x + 200
 4x = 200
 x = 50 km.

4. C
Explanation:
Let speed of the car be x kmph.
Then, speed of the train = (150/100) x = (3/2) x kmph.
75/x - 75/(3/2)x = 125/(10 x 60)
75/x - 50/x = 5/24
 x = (25 x 24)/5 = 120 kmph

5. B
Explanation:
Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9 x 60)/60 min = 10 min.

6. A
Explanation:
Let the duration of the flight be x hours.
Then, 600/x - 600/(x + 1/2) = 200
600/x - 1200(2x + 1) = 200
x(2x + 1) = 3
2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr [Neglecting the -ve value of x]

7. B
Explanation:
((1/2)/21)x + ((1/2)/24)x = 10
x/21 + x/24 = 20
15x = 168 x 20
x = (168 x 20)/15 = 224 km.

8. D
Explanation:
Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = 400/4 = 100
x = 100/8 = 12.5
Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.

9. Answer: Option C
Explanation:
Total time taken = 160/64 + 160/80 hrs. = 9/2 hrs.
Average speed = (320*2)/9 km/hr = 71.11 km/hr.


10. Answer: Option A
Explanation:
Let Abhay's speed be x km/hr.
Then, 30/x - 30/2x = 3
6x = 30
x = 5 km/hr.