A’s speed : B’s speed = 1¹⁄₂ : 1
= ³⁄₂ : 1
= 3 : 2
It means that in a race of 3 m, A gains (3 - 2).
= 1 m over B. 1 m is gained by A in a race of 3 m.

Correct Option: B

A’s speed : B’s speed = 1¹⁄₂ : 1
= ³⁄₂ : 1
= 3 : 2
It means that in a race of 3 m, A gains (3 - 2).
= 1 m over B. 1 m is gained by A in a race of 3 m.
∴ 300 m is gained by A in a race of = ³⁄₁ × 300 = 900 m.

When A makes 5 rounds, B makes 4 rounds.
In order to pass each other, the difference in number of rounds made by each must be one.
Here, A passes B each time, when A makes 5 rounds.
Distance covered by A in 5 rounds = 5 * 400 / 100 × = 2 Km.

Correct Option: D

When A makes 5 rounds, B makes 4 rounds.
In order to pass each other, the difference in number of rounds made by each must be one.
Here, A passes B each time, when A makes 5 rounds.
Distance covered by A in 5 rounds = 5 * 400 / 100 × = 2 Km.
In covering 2 Km, A passes B 1 time.
∴ In covering 5 Km, A passes B
= 5 / 2 = 2¹⁄₂ times.

While A runs 1000 m, B runs 1000 - 80 = 920 m and
while B runs 1000 m, C runs 1000 - 60 = 940 m.
∴ While B runs 920 m; C runs 940 × 920 / 1000 = 4324 / 5 m

Correct Option: A

While A runs 1000 m, B runs 1000 - 80 = 920 m and
While B runs 1000 m, C runs 1000 - 60 =940 m.
∴ While B runs 920 m; C runs
940 / 1000 × 920 = 4324 / 5 m
∴ While B runs 920 m; C runs 940 × 920 / 1000 = 4324 / 5 m
∴ While A runs 1000 m, C runs 4324 / 5 m
∴ A can beat C by 1000 - 4324 / 5 = 676 / 5 = 135¹⁄₅ m.

Let, times (in sec) taken by A and B to run a Km, be P and Q, respectively.
When B gets a start of 50 m, B runs.
1000 - 50 = 950 m while A runs 1000 m.

Correct Option: A

Let, times (in sec) taken by A and B to run a Km, be P and Q, respectively.
When B gets a start of 50 m, B runs.
1000 - 50 = 950 m while A runs 1000 m.
∴ 950 / 100 Q - P = 14,
i.e., 0.95Q - P = 14 …(1)
and, when B gets a start of 22 seconds, A runs for (Q - 22) seconds, while B runs for Q seconds.
∴ 1000 - 1000 / P (Q - 22) = 20
i.e., 50Q - 49P = 1100. …(2)
Multiplying Eq. (1) by 49 and subtract from Eq. (2)
3.45Q = 414
∴ Q= 120 sec.
∴ from (1)
⇒ P = 0.95 × 120 - 14 = 100 seconds.

Time taken by A to run 1 Km = 30 × 2 = 60 seconds.
Time taken by B to run 1 Km = 35 × 2 = 70 seconds.
∴ A can give B a start of (70 - 60) = 10 seconds.

Correct Option: C

Time taken by A to run 1 Km = 30 × 2 = 60 seconds.
Time taken by B to run 1 Km = 35 × 2 = 70 seconds.
∴ A can give B a start of (70 - 60) = 10 seconds.
In 35 sec B runs 500 m
∴ In 10 sec B runs = 500 × 10 / 35 = 1000 / 7 = 142⁶⁄₇ meters
So, A can give B a start of 142⁶⁄₇ meters in a Km race.