B runs 25 m in 5 seconds.
? B's time to cover 1 Km = 5 x 100 / 25 = 200 sec
A's time to cover one Km = 200 - 5 = 195 seconds
= 3 minutes 15 seconds.
From the question it is clear that speed of B = 15 / 5 = 3 m/s
The time taken by B to cover 300 m = 300 / 3 = 100 sec.
Hence, time taken by A to complete the race = 100 ? 5 = 95 sec.
In a game of 250 points, A scores 250 then B scores 200 points and C scores 180.
? B scores 250 points while C scores 180 x 250 / 200 = 225 points
Hence, in a game of 250 points B can give C (250 ? 225) = 25 points
In a game of 1000 meters, If A scores 1000 meters then B scores 950 meters and C scores 920 meters.
? B runs 1000 m while C scores 920 x 1000 / 950= 18400 / 19 m
Hence, in 1000 m race, B can give C (1000 - 18400 / 19) = 600 / 19 = 3111?19 meters start.
If A Score 100 then B scores 80 and C score 72.
? B scores 80 while C scores 72
? B scores 100 while C scores 72 * 100 / 80 = 90 points
Hence, in 100 points B can give (100 ? 90) = 10 points
If A run 1000 meters then B runs 900 meters and C runs 800 meters.
? B runs 1350 meters while C will run 800 * 1350/ 900 = 1200 meters
Hence, B can beat C by (1350 ? 1200) = 150 m
Suppose, P points make the game.
Clearly, when A scores P points, B scores (P - 20) points and C scores (P - 32) points.
Now, when B scores P points, C scores (P - 15) points.
When B scores (P - 20) points,
C scores [( P - 15 ) / P * P (P - 20)] points
? (P - 15)( P - 20) / P = P - 20 or, P = 100
Hence, 100 points make the game.
race remains to be run = 5 - 5?4 = 15?4 .
L.C.M. of 252, 308 and 198 = 2772 seconds
= 46 × 60 + 12 = 46 min 12 seconds.
.
Raju runs on Monday and Friday = 1250 × 2 = 2500 m
On Tuesday, Wednesday, Thursday and Saturday,
Raju runs 1500 × 4 = 6000 m
In 1 week Raju runs 6000 + 2500 = 8500 m
In 3 weeks Raju runs 3 × 8500 = 25500 m = 25.5 K
15 meter is covered by B in 5 sec
? 300 meter is covered by B in 5 × 300/15 = 100 seconds
? A takes 100 - 5 = 95 seconds.
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