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.

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.

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.

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.

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.

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.

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

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.

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

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.