CAT 2004 Question 18

Question 18

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 son standing form his father?


The three triangles are similar.

Let the distance of the tip of the shadow from the child be y. Let the child be standing at distance x from the father.

So, 6/(2.1+x+y) = 1.8/(x+y) = 0.9/y

=> 2y = x+y => x = y

=> 6/(2.1 + 2x) = 0.9/x

=> 6x = 0.9*(2.1+2x)

=> 6x = 1.89 + 1.8x

=> 4.2x = 1.89

=> x = 1.89/4.2 = 0.45


View Video Solution

Create a FREE account and get:

  • All Quant CAT Formulas and shortcuts PDF
  • 20+ CAT previous papers with solutions PDF
  • Top 500 CAT Solved Questions for Free


Register with


Boost your Prep!

Download App