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XAT 2014 — QA & DI Question 7

Simple EquationsEasy

There are two windows on the wall of a building that need repairs. A ladder 30 m long is placed against a wall such that it just reaches the first window which is 26 m high. The foot of the ladder is at point A. After the first window is fixed, the foot of the ladder is pushed backwards to point B so that the ladder can reach the second window. The angle made by the ladder with the ground is reduced by half, as a result of pushing the ladder. The distance between points A and B is

Answer & solution

  • A

    < 9 m

  • B

    ≥ 9 m and < 9.5 m

  • C

    ≥ 9.5 m and < 10 m

  • D

    ≥ 10 m and < 10.5 m

  • ≥ 10.5 m

Solution

The following figure represents the length and the position of the ladder,

​​​​​​​

By Pythagoras Theorem,

x=302-262=224≈15 m

∴cos 2θ=1530=12

⇒2θ=60°⇒θ=30°

cos 30°=y30

⇒32=y30

⇒y=153 m

The approximate distance between A and B can be given as,

y-x=153-15=10.98 m

Hence, option (e)

XAT 2014 QA & DI Q7: There are two windows on the wall of a building that need repairs. A ladder 30 m long is placed against a wall — Solution | TheCATExam