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Q:

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

A) 21 m	B) 26 m
C) 28m	D) 29m

Answer & Explanation Answer: C) 28m

Explanation:

A : B = 100 : 75

B : C = 100 : 96.

A : C = (A/B*B/C) = (100/75*100/96) = 100/72 =100:72

A beats C by (100 - 72) m = 28 m.

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Filed Under: Races and Games

Q:

A runs $1 \frac{2}{3}$ times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

A) 200 m	B) 300m
C) 270m	D) 160m

Answer & Explanation Answer: A) 200 m

Explanation:

Ratio of the speeds of A and B =5 : 1 = 5 :3

Thus, in race of 5 m, A gains 2 m over B.

2 m are gained by A in a race of 5 m.

80 m will be gained by A in race of $(\frac{5}{2} * 80)$ m =200m

=> Winning post is 200 m away from the starting point.

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Filed Under: Races and Games

Q:

A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a

king of heart is:

A) 2/13	B) 1/13
C) 1/26	D) 1/52

Answer & Explanation Answer: C) 1/26

Explanation:

Here, n(S) = 52.

Let E = event of getting a queen of club or a king of heart.

Then, n(E) = 2.

P(E) =n(E)/n(S)=2/52=1/26.

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Q:

A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:

A) 100 m	B) 75 m
C) 25 m	D) 50m

Answer & Explanation Answer: A) 100 m

Explanation:

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.

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Q:

In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:

A) 40 sec	B) 47sec
C) 33sec	D) none of these

Answer & Explanation Answer: C) 33sec

Explanation:

B runs 35 m in 7 sec.

B covers 200 m in (7/35*200) = 40 sec.

B's time over the course = 40 sec.

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

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Q:

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

A) 8 points	B) 10 points
C) 14points	D) 40points

Answer & Explanation Answer: B) 10 points

Explanation:

A : B = 100 : 80.

A : C = 100 : 72.

B:C = B/A*A/C = 80/10*100/72 = 10/9 = 100/90 = 100:90

B can give C 10 points

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Q:

Two dice are tossed. The probability that the total score is a prime number is:

A) 5/12	B) 1/6
C) 1/2	D) 7/9

Answer & Explanation Answer: A) 5/12

Explanation:

Clearly, n(S) = (6 x 6) = 36.

Let E = Event that the sum is a prime number.

Then E= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4,3),(5, 2), (5, 6), (6, 1), (6, 5) }

n(E) = 15.

P(E) = n(E)/n(S) = 15/36 = 5/12.

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Filed Under: Probability

Q:

In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:

A) 20m	B) 25m
C) 22.5m	D) 9m

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