Multiple choice

Passage

[CAT 1997] Directions for Questions 24 to 26: Answer the questions based on the following information. A certain race is made up of three stretches: A, B and C, each 2 km long, and to be covered by a certain mode of transport. The following table gives these modes of transport for the stretches, and the minimum and maximum possible speeds (in km/hr) over these stretches. The speed over a particular stretch is assumed to be constant. The previous record for the race is 10 min.

Mr.Tortoise completes the race at an average speed of 20 km/hr. His average speed for the first two stretches is four times that for the last stretch. Find the speed over stretch C.

  1. 15 km/hr

  2. 12 km/hr

  3. 10 km/hr

  4. This is not possible
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance = 6 km. Total time = 10 min = 1/6 hr. Average speed = 20 km/hr. Total time = 6/20 = 0.3 hr = 18 min. The record is 10 min, but the question asks for the speed based on the 20 km/hr average. Let speeds be v1, v2, v3. v1=v2 (first two stretches). Average speed for first two = v1. Average speed for last = v3. v1 = 4 * v3. Total time = 2/v1 + 2/v1 + 2/v3 = 4/v1 + 2/v3 = 4/(4v3) + 2/v3 = 1/v3 + 2/v3 = 3/v3. Total time = 6/20 = 0.3 hr. 3/v3 = 0.3, so v3 = 10 km/hr.

AI explanation

For Quantity I, the total marks of all 36 students across the three departments is 848 multiplied by 3, which equals 2544. The physics and chemistry departments have totals of 15 times 64 and 12 times 72, or 960 and 864 respectively. This leaves the total marks for the 9 maths students as 2544 minus 960 minus 864, equaling 720, making their average 80. For Quantity II, the total marks of the four students is 4 times 68, or 272. When the score of 76 is replaced by the correct score of 88, the new total becomes 284, making the actual average 71. Since 80 is greater than 71, Quantity I is greater than Quantity II.

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