Quantitative Aptitude

Quantitative Aptitude

1. A man travels first 50 km at 25 kmph, next 40 km at 20 kmph and then 90 km at 15 kmph. His average speed for the whole journey (in kmph) is:

(a) 25

(b) 20

(c) 18

(d) 40

2. A man walks at the rate of 5 km/hr for 6 hours and at 4km/hr for 12 hours. The average speed of the man (inkm/hr) is:

(a) 4 

(b) 4(1/3)

(c) 4(1/2)

(d) 4(2/3)

3. A boy goes to the school with the speed of 3 kmph and returns with the speed of 2 kmph. If he takes 5 hours in all, then the distance (in kms) between the village and the school is:

(a) 6

(b) 7

(c) 8

(d) 9

4. A is twice as fast as B and B is thrice as fast as C is. The journey covered by C in 42 minutes will be covered by A in:

(a) 14 min. 

(b) 7 min. 

(c) 28 min. 

(d) 54 min.

5. A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speeds is:

(a) 4 : 1 

(b) 1 : 4

(c) 2 : 1

(d) 1 : 2

6. A train takes 18 seconds to pass completely through a station 162 m long and 15 seconds through another station 120 m long. The length of the train (in metres) is:

(a) 70

(b) 80

(c) 90

(d) 100

7. Two trains whose lengths are 180 m and 220 m respectively are running in directions opposite to one another with respective speeds of 40 km/hr and 50 km/hr. Time taken by them in crossing one another will be:

(a) 16 sec

(b) 17 sec

(c) 18 sec

(d) 22 sec

8. A man standing on a railway platform observes that a train going in one direction takes 4 seconds to pass him. Another train of same length going in the opposite direction takes 5 seconds to pass him. The time taken (in seconds) by the two trains to cross each other will be:

(a) 31/9

(b) 40/9

(c) 49/9

(d) 50/9

9. A man rows upstream 11 km and downstream 26 km taking 5 hours each time. The velocity of the current is:

(a) 1 km/hr 

(b) 1.5 km/hr

(c) 2.5 km/hr

(d) 7.5 km/hr

10. A motor boat takes 2 hours to travel a distance of 9 km down the current and it takes 6 hours to travel the same distance against the current. The speed of the boat in still water and that of the current (in km/hr) respectively are:

(a) 3, 1.5

(b) 3, 2

(c) 3.5, 2.5

(d) 3, 1

Answers and Solution:
1. Total distance covered=(50+40+90)km=180 km.
Total time taken=(50/25+40/20+90/15)hrs=10 hrs.
∴  Average speed for the whole journey=(180/10)=18 kmph

2. Total distance covered=(5×6+4×12)km=78 km.
Total time taken=(6+12)hrs=18 hr.
∴Average speed=(78/18) km/hr=4(1/3) km/hr.
 
3.  Let required distance be x km. Then,
x/3+x/2=5 → x=6 km. 

4.Let C’s speed=x kmph, B’s speed=3x kmph & A’s speed = 6x kmph
∴ Ratio of speeds of A, B, C = 6x∶3x∶x = 6∶3∶1
Ratio of times taken=1/6 ∶ 1/3:1 = 1∶2∶6 .
If C takes 6 min, A takes 1 min.
If C takes 42 min, A takes (1/6×42) min = 7 min.

5.Let x km be covered in y hours. The,
1st speed=(x/y)kmph,2nd speed=(x/2 *1/2y)=(x/4y) kmph
∴  Ratio of speeds=x/y ∶ x/4y=1∶1/4=4∶1

6.Let the length of the train be x metres.
(x+162)/18 = (x+120)/15→15(x+162)=18(x+120)→x=90

7.Relative speed=(40+50)kmph=(90×5/18)m/sec =25 m/sec
Required time=Time taken to cover (180+220) m at 25 m/sec. =(400/25)=16 sec.

8.Let the length of each train be x metres.
The, speed of first=(x/4)m/sec, speed of 2nd=(x/5)m/sec
Relative speed=(x/4+x/5)m/sec=(9x/20)m/sec⁡   
Time taken to cross each other
=time taken to cover 2x metres at (5x/12)m/sec
=(2x*20/9x)sec=(40/9)sec.

9.Rate upstream=(11/5)kmph=2.2 kmph
Rate downstream=(26/5)kmph=5.2 kmph.
∴  Velocity of current=1/2(5.2-2.2)kmph=1.5 kmph.

10. Rate downstream=(9/2)kmph = 4.5 kmph
Rate upstream=(9/6)kmph=1.5 kmph
∴ Rate in still water=1/2(4.5+1.5)kmph=3 kmph

Rate in current=1/2(4.5-1.5)kmph=1.5 kmph