Q. 23 The traffic lights at three different road crossings change after 24 seconds, 36 seconds and 54 seconds respectively. If they all change simultaneously at 10.15 a.m., then at what time will they again change simultaneously?

Q. 24 Four runners started running simultaneously from a point on a circular track. They took 200 seconds, 300 seconds, 360 seconds and 450 seconds to complete one round. After how much time do they meet at the starting point for the first time?

Q. 29 Three sets of English, Mathematics and Science books containing 336, 240, 96 books respectively have to be stacked in such a way that all the books are stored subject-wise and the height of each stack is the same. The total number of stacks will be

Answer: (C) 4/35 Explanation: Let the two numbers be x and y then xy = 3 * 105 = 315 and x + y = 36 (given) hence (x + y)/xy =36/315 or (1/x) + (1/y) = 4/35

Q. 32 Let x be the smallest number, which when added to 2000 makes the resulting number divisible by 12, 16, 18 and 21. The sum of the digits of x is

Answer: (D) xyz Explanation: Ratio of the number = x : y and HCF of the two numbers = z Let the two numbers be xz and yz Product of the two numbers = LCM * HCF or, LCM = (xz * yz)/z = xyz

Q. 39 Three numbers are in the ratio 1 : 2 : 3 and their HCF is 12. The numbers are