Quantitative Aptitude Ques 1396

Question: If $ P(a,0), $ $ Q(0,b) $ and $ R(1,1) $ are collinear, then find the value of $ \frac{1}{a}+\frac{1}{b} $

Options:

A) $ 2 $

B) $ 1 $

C) $ -1 $

D) $ 0 $

Show Answer

Answer:

Correct Answer: B

Solution:

  • Since, P, Q and R are collinear

$ \therefore $ Area of $ \Delta PQR=0, $ then $ \frac{1}{2}[x _1(y _2-y _3)+x _2(y _3-y _1)+x _3(y _1-y _2)]=0 $

$ \therefore $ $ x _1=a, $ $ x _2=0, $ $ x _3=1, $ $ y _1=0, $ $ y _2=b $ and $ y _3=1 $

$ \Rightarrow $ $ \frac{1}{2}[a\times (b-1)+0\times (1-0)+1\times (0-b)]=0 $

$ \Rightarrow $ $ \frac{1}{2}[ab-b-a]=0 $
$ \Rightarrow $ $ ab=a+b $

$ \Rightarrow $ $ 1=\frac{a+b}{ab} $
$ \Rightarrow $ $ \frac{1}{a}+\frac{1}{b}=1 $

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