Race

Question 1

Ram and Shyam participate in a race of 200m. If Ram starts when Shyam has covered 25 meters, then Ram finishes the race 10 seconds before Shyam and if Ram starts when Shyam has covered 45 meters then both finish the race at the same time. How long does Ram take to run 200m?

• A. 120
• B. 77.5
• C. 87.2
• D. 100

Answer: (B)

Let time taken by Ram be Tr seconds to cover 200m.   For first case, Shyam will be covering 175m in (Tr+10)sec (As it is given that Ram takes 10sec less than Shyam) So speed of Shyam is (175/Tr+10) m/s.   For second case, Shyam will take Tr seconds to cover 155m (200-45)   so speed of Ram is (155/Tr) m/s   Equating both speed of Ram we get 175Tr = 155(Tr+10) => Tr=77.5 s  

Question 2

If Geeta can give a start of 100 m of distance or 20 s of time to her friend Meena in a race of 1000 meters. How much time Geeta will take to cover the 1000 meters?

• A. 200 sec
• B. 160 sec
• C. 180 sec
• D. 140 sec

Answer: (C)

That means Meena will cover 100 m in 20 sec
=> meena can cover 1000 m in = 200 secs
Geeta can give a start of 100 m or 20 sec to Meena
=> Geeta will take 20 sec less than Meena
=> Geeta will take 180 sec to cover 1000 meters.

Question 3

Sita and Radha participate in a race of 1000 m. If Sita starts, when Radha has covered 100 meters, then Sita finishes the race 20 seconds before Radha, and if Sita starts, when Radha has covered 125 meters then both finish the race at the same time. How long does Sita take to run the complete race?

• A. 350
  
• B. 700
  
• C. 780
  
• D. 900
  

Answer: (B)

Let time taken by Sita be Ts seconds to cover 1000m.   

For first case, Radha will be covering 900m is (Ts+20)sec (As it is given that Sita takes 20sec less than Radha)   

So speed of Radha is (900/Ts+20) m/s   

For second case, Radha will take Ts second to cover 875m (1000-125)   

so speed of Radha is (875/Ts) m/s   

Equating both speed of Radha we get 900Ts = 875(Ts+20) => Ts=700 sec.

Question 4

If Mohan can give a start of 50 m of distance or 10 s of time to Rohan in a race of 1000 meters. How much time Mohan will take to cover the 1000 meters?

• A. 190 sec
• B. 200 sec
• C. 240 sec
• D. 180 sec

Answer: (A)

That means Rohan takes 10 sec to cover 50 meters
=> Rohan will cover 1000 meters in 200 sec
Mohan is giving a start of 10 sec. means Mohan will take 10 sec less than Rohan to cover 1000 m.
so, Time taken by Mohan to cover 1000 m is 190 sec.

Question 5

Ram and Sita participate in a race of 1000 meters. If Ram gives Sita a start of 200 meters or 20 seconds. In ow much time Ram completes the race?

• A. 70 sec
• B. 120 sec
• C. 100 sec
• D. 80 sec

Answer: (D)

Sita takes 20 sec. to run 200 m.
=> Sita takes 100 sec. to run complete 1000 m.
Ram gives Sita a start of 20 sec, means Ram is able to complete the race in 20 sec. less time than Sita
=> Ram will take 80 sec.