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.
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.
Let us assume A cover P meter in the time after which he meets with B.
According to question,
Time taken by A to cover the P distance = Time taken by B to cover the 4200 - P distance.
Use the distance and time formula
P / 500 = (4200 - P ) / 700
Or 700P = 500 x 4200 - 500P
Or 700P + 500P = 500 x 4200
Or 1200P = 500 x 4200
Or 12P = 5 x 4200
Or P = 5 x 4200 / 12
Or P = 5 x 350
Or P = 1750 meters
Required time taken by A to cover 1750 meters = 1750 / 500 = 175/50
Required time taken by A to cover 1750 meters = 3.5 minutes.
A scores 100 while B scores 100 - 20 = 80 and C scores 100 - 28 = 72.
? While B scores 80, C scores 72.
? While B scores 100, C scores 72 × 100 / 80 = 90.
? B can give C 100 - 90 = 10 points.
A : B : C = 90 : 75 : 60
B:C = 75 / 60 = ( 75 x 100?75 ) / ( 60 x 100?75) = 100 / 80
Hence, in a game of 100 points, B can give C(100 - 80)
= 20 points.
Total speed of car, bus and train = 72 × 3 = 216 Km
Speed of car and train = ( 5 + 9 ) x 216 / ( 5 + 9 + 4 ) = 168 Km
Average = 168 / 2 = 84 Km
A : B = 100 : 90.
A : C = 100 : 87.
B/C = (B/A*A/C) = (90/100*100/87) = 30/29
When B runs 30 m, C runs 29 m.
When B runs 180 m, C runs (29/30*180)m =174m
B beats C by (180 - 174) m = 6 m.
B covers 28 meters in 7sec. So, B's time over the course = (7/28)*100 =250 sec.
Whereas A's time over the course = 250 -7 = 243 sec.
i.e A's time over the course is 4min , 3 sec.
When B runs 25 m, A runs 45/2 m
When B runs 1000 m, A runs (45/2*1/25*1000)m = 900 m.
B beats A by 100 m.
A's speed = (5*5/15)m/sec = (25/18)m/sec
Time taken by A to cover 100 m = (100*18/15)sec = 72sec
Time taken by B to cover 92 m = (72 + 8) = 80 sec.
B's speed =(92/80*18/5)kmph =4.14kmph
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