A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son’s head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post, then how far (in metres) is the son standing from his father?  Choose the correct choice from the following options:
A) 0.9  B) 0.75  C) 0.6  D) 0.45  E) None of these
Explanation :   L is the lamp post position, F is father and S is son’s position. X is the point where the shadow falls.   LD = 0.9 = Son’s height , LB = 1.8 = Father’s height.   So AB = 6 – 1.8 = 4.2 Also BC = LF = 2.1   We observe that ∆ABC ~ ∆ADE (two triangles are similar).   Hence, the corresponding sides are proportional.   So, AB/AD = DC/DE.   4.2/5.1 = 2.1/DE.   DE = 5.1*2.1/4.2 = 5.1/2 = 2.55.   LS = DE = 2.55   FS = LS – LF = 2.55 – 2.1 = 0.45.   Answer : 0.45
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A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son’s head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post, then how far (in metres) is the son standing from his father?