MCQ: Races and Games of Skill - 2 - SSC CGL MCQ

A : B = 100 : 90.
A : C = 100 : 87.

When B runs 30 m, C runs 29 m.
When B runs 180 m, 

∴ B beats C by (180 - 174) m = 6 m.

B runs 35 m in 7 sec.

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

A : B = 100 : 80.
A : C = 100 : 72.


∴ B can give C 10 points.

Clearly, B covers 40 m in seconds.
∴ B's time over the course = (8/40*1000) sec. = 200sec.
A's time over the course = (200-8) sec. =192 sec. = 3 min. 12 sec.

Time taken by A to run 100m = (60*60/6000*100) sec. = 60 sec.
B covers (100-4) m in (60 +12) sec.
∴ B's speed = 96/72m/sec. = (96/72*18/5) km/hr = 4.8 km/hr

Time taken by A to run 1 km = 290 sec.
Time taken by B to run 1 km = 300 sec.
A can give B a start of (300-290) = 10sec.
In 300 sec, B runs (1000/300*10) m = 100/3 m
∴ A can give B start of 100/3 m.

Clearly, A beats B by 10 sec.
Distance covered by B in 10 sec. = (1000/200*10)m = 50m 
∴A beat B by 50 m.

While A covers 1000m, B covers (1000-40)=960m and C covers (1000-64) = 936m.
When B covers 960 m, C covers 936 m.
When B covers 1000m, C covers (936/960*1000)m = 975m
∴ B gives C a start of (1000-975) m = 25 m.

If A runs 600m, B runs 540 m.
If A runs 400m, B runs (540/600*400) m = 360m 
When B runs 500m, C runs 450m.
When B runs 360 m, C runs (450/500*360) m = 324 m.
∴ A beats C by (400-324) m =76 m.

Distance covered by B in 3 sec. =(100/30*3) m = 10m 
∴ A beats B by 10m.

Distance covered by B in 6 sec. =(1000/300*6)m = 20m
∴  A beats B by 20 m.
For a dead heat race, A must give B a start of 20m.

Ratio of the rates of A and B = 7:4
3m are gained by A in a race of 7m .
60m  are gained by A in a race of (7/3*60)m = 140m.

A: B :C = 60:45: 40
∴  B:C = 45/40 =9/8 = 9*10/8*10 = 90/80
Thus , if B score 90 points , then C score 80 points.
B can give C 10 points in a game of 90.

In a 25m race, B beats A by 5 m.
In a km race , B beats A by (5/25*1000) m = 200m

A's  speed  =(5*5/18) m/s = 25/18m/s.
Time taken by A to cover 100m  = (100* 18/25) sec.  =72 sec.
∴ B covers 92 m in (72+8) sec.= 80 sec.
∴ B's speed = (92/80)m/sec. = (92/80* 18/5) km/hr =  4.14km/hr