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The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is: A. 276 B. 299 C. 322 D. 345 Clearly, the numbers are (23 x 13) and (23 x 14).  Larger number = (23 x 14) = 322.
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A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long? A. 65 sec B. 89 sec C. 100 sec D. 150 sec Answer: Option B Explanation: Speed = 240 m/sec = 10 m/sec. 24 Required time = 240 + 650 sec = 89 sec.
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Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: A. 1 : 3 B. 3 : 2 C. 3 : 4 D. None of these Answer: Option B Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x metres, and length of the second train = 17 y metres. 27 x + 17 y = 23 x + y 27 x + 17 y = 23 x + 23 y 4 x = 6 y x = 3 . y 2
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The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: A. 200 m B. 225 m C. 245 m D. 250 m Answer: Option C Explanation: Speed = 45 x 5 m/sec = 25 m/sec. 18 2 Time = 30 sec. Let the length of bridge be x metres. Then, 130 + x = 25 30 2 2(130 + x ) = 750 x = 245 m.
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A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

.  A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: A. 45 km/hr B. 50 km/hr C. 54 km/hr D. 55 km/hr Answer: Option B Explanation: Speed of the train relative to man = 125 m/sec 10    = 25 m/sec. 2    = 25 x 18 km/hr 2 5    = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = ( x - 5) km/hr. x - 5 = 45         x = 50 km/hr.
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