Xavier Aptitude Test 2019 Paper

Question : 66 of 98

Marks: +1, -0

The figure below shows two right angled triangles ΔOAB and ΔOQP with right angles at vertex A and P, respectively, having the common vertex O. The lengths of some of the sides are indicated in the figure. (Note that the figure is not drawn to scale.) AB and OP are parallel.
What is ∠QOB?

60°
30°
$\tan^{-1}2/3$
45°
$\tan^{-1}3/2$

Validate

Solution:

\tan α =1/3,\tan β=1/2

\tan (α+β)={\tan α+\tan β}/{1-\tan α\tan β}

={1/3+1/2}/{1-(1/3×1/2)}={5/6}/{5/6}=1

∴α+β=45°

Now, ∠QOB = 90° - (α + β) = 90° - 45°= 45°

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