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Races & Games of Skill

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11.

In a 100 m race, P can give Q 20 m and R 32 m. In the same race Q can give R:

Answer: C

P : Q = 100 : 80.
P : R = 100 : 68.
Q : R = Q/P * P/R
= (80/100) * (100/68)
= 80/68
When Q runs 80 m, R runs 68 m.
When Q runs 100 m, R runs ((68/80) * 100)m = 85m
Q can give R 15 m.

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12.

In a 550 m race, the ratio of the speeds of two contestants P and Q is 3 : 4. P has a start of 170 m. Then, P wins by:

Answer: B

To reach the winning post A will have to cover a distance of (550 - 170)m, i.e., 380 m.
While P covers 3 m, Q covers 4 m. (380 * (4/3)) = 506
While P covers 440 m, Q covers
Thus, when P reaches the winning post, Q covers 506 m and therefore remains 44 m behind.
P wins by 44 m.

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13.

In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?

Answer: B

Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.

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14.

In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C :

Answer: B

No answer description available for this question.

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15.

In a 100 m race, A can give B 10 m and C 28 m. In the same race, B can give C

Answer: A

"A can give B 10 m".
In a 100 m race, while A starts from the starting point, B starts 10 meters ahead from the same starting point at the same time.
"A can give C 28 m"
In a 100 m race, while A starts from the starting point, C starts 28 meters ahead from the same starting point at the same time.
i.e., in a 100-10=90 m race, B can give C 28-10=18 m
In a 100 m race, B can give C 18/90×100 = 20 m

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16.

In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:

Answer: C

In a game of 100 points, A scores 100 points, B scores (100-20)=80 points and C scores (100-28)=72 points
i.e., when B scores 80 points, C scores 72 points
When B scores 100 points, C scores 72/80×100 = 90 points
i.e., In a game of 100 points, B can give C (100-90)=10 points

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17.

In a 500 m race, A reaches the final point in 28 s and B reaches in 35 s. By how much distance does A beat B?

Answer: A

In this question, we have to find the distance covered by B, after A has finished the race i.e. distance covered by B in (35 – 28 = 7s).
Distance = 500/35 × 7 = 100m
A beats B by 100 m.

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18.

In a race of 300 metres A rates B by 15 metres or 5 seconds, Hoe much time A take to complete the race?

Answer: C

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.
 

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19.

In a game of 100 points, A can give B 20 points and C 28 points. Number of points B can give C in a game of 100 points is

Answer: A

A scores 100 while B scores 100 - 20 = 80 and C scores 100 - 28 = 72.
While B scores 80, C scores 72
While B scores100, C scores72/80 x 100 = 90
B can give C 100 - 90 = 10 points.

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20.

In a 100m race, A can beat B by 25m and B can beat C by 4m. In the same race, A can beat C by

Answer: D

A :B = 100:75 and B :C = 100:96
A :C = (A/B * B/C ) = (100/75*100/96 ) = 100/72 = 100:72
So, A beats C by (100-72) m = 28m

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