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Q #6
:

Directions: Read the following information to answer the question.

Abhay, Ajay and Vijay wish to travel from town A to town B. They have one motorcycle which can be driven by any of them but can carry only two persons at a time. The distance between the two towns is 105 km and the speed at which they can walk is 5 kmph. If the speed of the motorcycle is 35 kmph then what is the total distance that the bike travels if they travel such that all three of them reach town B simultaneously?

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If speed of bike = 35 kmph

    i.e., the bike travels 7 times as fast as they can walk 

    then CD + DB = 7CB

    ⇒ DC = 3x (let CB = x)

    IIIly AD = x

    ⇒ AB = 5x = 105 km  ⇒ x = 21 km

    The bike travel AC + CD + DB = 11x = 11 x 21

 


Q #7
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Directions: Read the following information to answer the question.

A man set out at noon to walk from Khalagpur to Danapur, and a friend of his started at 2 pm on the same day to walk from Danapur to Khalagpur. They met on the road at five minutes past four o’clock, and each man reached his destination at exactly the same time. Can you say at what time they both reached their respective destinations?

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Q #8
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Directions: Read the following information to answer the question.

A clock is observed. The hour hand is exactly at the minute mark, and the minute hand is six minutes ahead of it. Later, the clock is observed again. This time the hour hand is exactly on a different minute mark, and the minute hand is seven minutes ahead of it. How much time has elapsed between the first and the second observation?

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Solution The hour hand is exactly on a minute mark five times per hour -- on the hour, twelve minutes past the hour, twenty four minutes past, thirty six minutes past, and forty eight minutes past. Let X be the number of hours, and Y be the number of minutes past the hour. When the hour hand is on a minute mark, the position of the hour hand is 5X + Y/12, and the position of the minute hand is Y. On the first occasion, Y = 5X + Y/12 + 6. This is equivalent to 60X = 11Y - 72. Since Y can only take one of the values in the set { 0, 12, 24, 36, 48 }, it can be determined that the only legal values for the equation are X = 1 and Y = 12. So the time is 1:12. Similarly, the second occasion's equation is 60X = 11Y - 84. The only legal values here are X = 3 and Y = 24. So the time is 3:24. Between 1:12 and 3:24, two hours and twelve minutes have elapsed.

Q #9
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Directions: Read the following information to answer the question.

You begin your vacation at Village A and travel to Village B. From Village B you move on to Village C and then to Village D. You leave Village D and return back to Village A. Your round trip was 54 km and the distance between each village is a whole number. The distance between Village A and Village B is greater than between Village B and Village C Also, if you went directly from Village B to Village D, it would be a distance of 12 km. What is the distance from Village C to Village D?

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Q #10
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Directions: Read the following information to answer the question.

There are two concentric circular tracks of lengths 200 km. and 300 km. A car moves on the outer track at the speed of 50 kmph in the clock wise dirdction. A scooter moves on the inside track in the anti-clockwise direction at a speed of 60 kmph. If both start from the north most point of the track at the same time and the first person to travel 1200 km does so and stops, then how many times has he crossed the other person in the time in which he was moving?

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