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01. In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is: 
A. 86 sec B. 80 sec
C. 76 sec D. None of these

Answer and Explanation

Answer: 80 sec

Explanation:
B runs 45/2 m in 6 sec.

B covers 300 m in 6 x (2/45) x 300 sec = 80 sec.

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02. In a 200 metres 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 and Explanation

Answer: 33 sec

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.

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03. In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by: 
A. 22.75 m B. 25 m
C. 19.5 m D. 7 4/7 m

Answer and Explanation

Answer: 25 m

Explanation:
A : B = 200 : 169.
A : C = 200 : 182.
C/B = (C/A) x (A/B)   = 182/200 x 200/169   = 182 : 169.

When C covers 182 m, B covers 169 m.
When C covers 350 m, B covers (169/182) x 350 m = 325 m.

Therefore, C beats B by (350 - 325) m = 25 m.

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04. 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 and Explanation

Answer: 20 m

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 360 m = 480 m.

Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.
A wins by 20 m.

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05. In a race of 800m, if the ratio of the speeds of two participants P and R is 3:4, and P has a start of 120m, then R beats P by:
A. 100m B. 80m
C. 90m D. 110m

Answer and Explanation

Answer: 80m

Explanation:
As P has a start of 120m, P has to cover 680m while R has to cover 800m.
Now, when P covers 3m, R covers 4m.
Hence, when R covers 800m, P covers (800 * 3) / 4 = 600m
Therefore, R beats P by 80m.

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06. If in a race of 120m X can beat Y by 20m and Z by 35m, then Y can beat Z by:
A. 12m B. 10m
C. 15m D. 18m

Answer and Explanation

Answer: 18m

Explanation:
In a race of 120m, as X beats Y by 20m, when X runs 120m, Y runs 100m.
Similarly, as X beats Z by 35m, when X covers 120m, Z covers 85m.
Hence, when Y runs 100m, Z runs 85m.
When Y runs 120m, Z runs (120 * 85) / 100 = 102m
Hence, Y beats Z by 18m.

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07. Three persons, A, B and C with speeds 10, 15 and 20 km/hr respectively run around a circular track of 1000m. If they started the race from the same point at the same time and run in the same direction, find when they will meet for the first time.
A. 12 min B. 11 min 
C. 12.5 min D. 13 min

Answer and Explanation

Answer: 12 min

Explanation:
Length of the track, L = 1km
Speed of A = 10 km/hr; Speed of B = 15 km/hr and speed of C = 20 km/hr
Since 20 > 15 > 10
We have, the time taken to meet for the first time =
LCM of (L / c-b , L / b-a)
L/c-b = 1/20 – 15 = 1/5
L/b-a = 1/15 – 10 = 1/5
LCM of both is 1/5 hours, i.e. 12 min
They will meet for the first time, 12 minutes after they start

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08. A and B are running around in a circular track in opposite directions. They meet at a point 450 m from the starting point and continue running. They now meet at a point 200 m from the starting but, in the opposite direction as before. What is the length of the track if A is yet to complete one round?
A. 1600m B. 1200m 
C. 1750m D. 1500m

Answer and Explanation

Answer: 1200m 

Explanation:
Let the length of the track be L m. it is obvious that B is faster than A
As A has not yet completed one round around the circle but B has While A travels 450 m, B travels L – 450m. After meeting for the first time, B continues and travels 450 m + 300 m = 750 m, while A travels (L – 450) – 300 = L – 750 m.
Let speed of A be ‘a’ m/s and speed of B be ‘b’. Relative speed = (a + b) m/s
Time taken for B to travel ( L -450)m = Time taken for B to travel 450 m.
(L-450) / b = 450 / a --> (1)
Time taken for A to travel L – 750m = Time taken for B to travel 750 m,
750 / b = L – 750 / a -->(2)
Equating for L and solving, we get a/b = 450/750
When a covers 1m, B covers (750/450) m.
Hence when A covers 450 initial, B covers 750 m and total length of track = 450 + 750 = 1200 m.

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09. A and B can run around a circular track in 6 and 8 minutes. If they start together and run in the same direction, when will they meet each other for the first time?
A. 16min  B. 48 min  
C. 24 min  D. Indeterminate

Answer and Explanation

Answer: 24 min 

Explanation:
 Let the length of track = L m
Speed of A = L/6 m/min; Speed of B = L/8 m/min
Since they are running in the same direction,
Time taken to meet for first time =
L / (L/6 – L/8) = L / (4L – 3L)/24 = 24L/L = 24 min
Alternately, time taken to meet for the first time = LCM (6 minutes, 8 minutes) = 24 mins

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10. In a 500 m race, the ratio of speed of two runners P & Q is 4:5. If P has a start of 100m, then what is the distance between P and Q at the finish of the race?
A. 100m  B. Both finish the race at the same time  
C. 50m D. 25m

Answer and Explanation

Answer: Both finish the race at the same time  

Explanation:
 (Speed of P) / (Speed of Q) = 4/5
In the time P runs 400 , Q runs 500m. but P has a start of 100m and he has another 400m to cover. In the time taken by P to cover this, Q can cover the entire 500 m, thus finishing the race with P.
P and Q finish the race at the same time.

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