Race & Games

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Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.


1. In a game of 60, A can give B 6 points. How many points can A give B in a game of 100?

A. 6

B. 8

C. 10

D. 12


Answer

                  Ans: Option C

       Explanation:

       When A gets 60 points, B gets 54.

       When A gets 100 points, B gets( 54*100)/60 = 90

       A can give 10 points. 


2. A can run 220 meters in 41 seconds and B in 44 seconds. By how many seconds will B win if he has 30 meters start?

A. 8 sec

B. 4 sec

C. 2.5 sec

D. 3 sec


Answer

                  Ans: Option D

       Explanation:

       B has a start of 30 meter.

       A has to run 220 meter and B has to run (220-30)=190 meter

       Given that A takes 41 seconds to cover this 220 meter.

       B takes 44 seconds to cover 220 meter.

    B takes 44/220 seconds to cover 1 meter

    => B takes (44/220)×190

                    =(4/20)×190

                    = 38 seconds to cover 190 meter

       i.e., A beats B by (41-38) = 3 seconds 


3. In a 100 m race, A reaches the winning post in 30 seconds and beats B by 10 m. Find the time taken by B to reach the winning post.

A. 33.33 s

B. 36 s

C. 40 s

D. 45 s


Answer

                  Ans: Option A

       Explanation:

       B was 10 m behind when A finished the race.

       B ran 90 m in 30 seconds.

       Time taken by B to run 100 m = 100*(30/90) = 33.33 s 


4. In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:

A. 18 m

B. 20 m

C. 27 m

D. 9 m


Answer

                  Ans: Option B

       Explanation:

       A : B = 100 : 90.

       A : C = 100 : 72.

       B : C =(B/A.x(A/C.=(90/100)x(100/72)=(90/72)       .

       When B runs 90 m, C runs 72 m.

       When B runs 100 m, C runs (72/90)x 100m = 80 m.                

       B can give C 20 m. 


5. The speeds of Daniel and Robert are in the ratio 3:4. In a 300 m race, Daniel has a start of 90 m. Daniel won the race by

A. 30 m

B. 20 m

C. 15 m

D. 10 m


Answer

                  Ans: Option B

       Explanation:

       To reach the winning post, Daniel has to run 300-90 = 210m

       Time taken by Daniel to run 210m = 210/3x = 70/x.

       Distance covered by Robert in (70/x) seconds = (70/x)*4x = 280m

       Hence, Daniel won by 20 m. 


6. A can run 224 meter in 28 seconds and B in 32 seconds. By what distance A beat B?

A. 36 meter        

B. 24 meter

C. 32 meter        

D. 28 meter


Answer

                  Ans: Option D

       Explanation:

 Clearly, A beats B by 4 seconds

Now find out how much B will run in these 4 seconds

Speed of B = Distance time taken by B=224/32=28/4=7 m/s

Distance covered by B in 4 seconds = Speed × time =7×4=28 meter

i.e., A beat B by 28 meter 


7. In a race, A beats B by 20 m or 10 seconds. Find B's speed.

A. 4 m/s

B. 5 m/s

C. 2 m/s

D. 2.5 m/s


Answer

                  Ans: Option C

       Explanation:

       20 meters are covered by B in 10 seconds.

       B's speed = 20/10 = 2 m/s 


8. In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:

A. 60 m

B. 40 m

C. 20 m

D. 10 m


Answer

                  Ans: Option C

       Explanation:

       To reach the winning post A will have to cover a distance of

                                                              (500 – 140)m, i.e., 360 m.

       While A covers 3 m, B covers 4 m.

       While A covers 360 m, B covers   (4/3)x 360m= 480 m.

    Thus, when A reaches the winning post, B covers 480 m

    and therefore remains 20 m behind.

        Hence, A wins by 20 m. 


9. The time taken by P to run 50 m is equal to the time taken by Q to run 75 m. In a 600 m race, Q beats P by

A. 100 m

B. 250 m

C. 150 m

D. 200 m


Answer

                  Ans: Option D

       Explanation:

       When Q runs 75 m, P runs 50 m.

       When Q runs 600 m, P runs 600*50/75 =400 m

       Q beats P by 200 m 


10. In a 100 m race, A runs at 6 km/hr. A gives B a start of 4 m and still beats him by 4 sec. Find the speed of B.

A. 4.6 km/hr       

B. 5.6 km/hr

C. 4.4 km/hr       

D. 5.4 km/hr


Answer

                  Ans: Option D

       Explanation:

       Speed of A = 6 km/hr = (6×1000)/(60*60)= 5/3 m/s

       Time taken by A = distance * speed= 100*(5/3) =60 sec

       A gives B a start of 4 m

i.e., B has to cover (100-4) = 96 meter

       A beats B by 4 sec

Time taken by B to run the race = 60 + 4 = 64 sec

       Speed of B = Distance/ time=96m/64s

                          = (96*1000)/(64*3600)

                          =(96*10)/(64*36)

                          =5.4 km/hr 


11. In a race, A beats B by 20 m or 10 seconds. Find B's speed.

A. 4 m/s

B. 5 m/s

C. 2 m/s

D. 2.5 m/s


Answer

                  Ans: Option C

       Explanation:

       20 meters are covered by B in 10 seconds.

       B's speed = 20/10 = 2 m/s 


12. In a 200 meters race A beats B by 35 m or 7 seconds. A's time over the course is:

A. 40 sec     

B. 47 sec

C. 33 sec     

D. None of these


Answer

                  Ans: Option C

       Explanation:

       B runs 35 m in 7 sec.

       B covers 200 m in(7/35)x 200= 40 sec.

       B's time over the course = 40 sec.

       A's time over the course (40 – 7) sec = 33 sec. 


13. In a game of cards, A can give B 10 points in 50 and A can give C 20 points in 60. How many points can B give C in a game of 90?

A. 25

B. 50

C. 30

D. 18


Answer

                  Ans: Option A

       Explanation:

       A:B = 50:40

       A:C = 60:40

       B:C = (B/A)*(A/C) = (40/50)*(60/40) = 60/50

If B gets 60 points, C gets 50. If B gets 90 points gets 90*(50/60) = 75

B can give C 25 points in a game of 90. 


14. A runs 4/3 as fast as B. If A gives B a start of 30 meters. How far must be the winning post, so that the race ends in a dead heat?

A. 100 m             

B. 110 m

C. 140 m             

D. 120 m


Answer

                  Ans: Option D

       Explanation:

       Let the distance to the winning point = x

       Speed of A: Speed of B = 4/3 : 1

       Let Speed of A = 4k/3

       Speed of B = k

A gives B a start of 30 meters

=> A run x meters and B run (x-30) meters

Time taken by A=Distance run by A Speed of A= x (4k3)

Time taken by B=Distance run by B Speed of B=x−30k

For the race to be a dead-heat race,

         Time taken by A = Time taken by B

         ⇒x (4k3)=x−30k

         ⇒x(43)=x−30

         ⇒3x=4x−120

         ⇒x=120

i.e., the distance to the winning point = 120 meter 


15. The speeds of A and B are in the ratio 3:4. B gives A a start of 30 m. How far should the winning post be so that the race ends in a dead heat?

A. 100 m

B. 200 m

C. 150 m

D. 120 m


Answer

                  Ans: Option D

       Explanation:

       Let A's speed be 3x m/s and B's speed be 4x m/s.

       Let the distance of the winning post be k m.

       Time taken by A to finish the race = (k-30)/3x

       Time taken by B to finish the race = k/4x

For the race to end in a dead heat, (k-30)/3x = k/4x Solving, k = 120 m

 


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