0Concept 6: Application of AM-GM in TSD
Using AM & HM in proportionality relations,Quite often in questions we find that the given speeds (or time taken) are in an Arithmetic Progression. And if distance covered at the speeds is constant, then time taken (or speeds) will be inversely proportional i.e. they will be in Harmonic Progression.
For those who have forgotten, the Arithmetic Mean of a and b is(a + b)/2 and the Harmonic Mean of a and b is 2ab/(a+b)
Though it requires a little trained eyes to identify the above, it will be useful if you keep a watch for it. See the following data to realise that either time taken or speeds are in an Arithmetic Progression.
E.g: 1. If I travel at 15 kmph, I reach office at 10 am,if I travel at 10 kmph, I reach office at 10:30 am. At what speed should I travel so that I reach office at 10:15. Assume I leave home at same time and take the same route. ( Use am/hm -- no other method)
Solution . Leaving at same time and reaching at 10 am, 10:15 am and 10:30 am suggests that the time travelled are in AP. Thus, speeds are in HP and required speed is the,
HM of 10 & 15
i.e.2 *10 *15/25 = 12 kmph
