In a game of 250 points A can give B 50 points and C 70 points. In the same game how many points can B give C?

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

The distance covered by B in 35 seconds = 200 x 35 / 38 = 3500 / 19 m
Now, 200 ? 3500 / 19 = 300 / 19 = 15¹⁵?₁₉ m Hence, A can beat B by 15¹⁵?₁₉ m.

When B runs 50 m, then A runs 45 m.
When B runs 1000 m, then A runs (45/50) x 1000 m = 900 m
? B beats A by 100 m.

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.

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.

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.
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