Quantitative Aptitude Ques 1041

Question: There are two circles of radii $ r _1 $ and $ r _2(r _1<r _2). $ The area of the bigger circle is $ \frac{693}{2}cm^{2}. $ The difference of their circumferences is $ 22cm. $ What is the sum of the diameters of the two circles?

Options:

A) 17.5 cm

B) 22 cm

C) 28.5 cm

D) 35 cm

Show Answer

Answer:

Correct Answer: C

Solution:

  • According to the question, $ \pi r_2^{2}=\frac{693}{2} $
    $ \Rightarrow $ $ r_2^{2}=\frac{693}{2}\times \frac{7}{22} $

$ \Rightarrow $ $ r _2=\sqrt{\frac{693\times 7}{2\times 22}} $

$ \therefore $ $ d _2=2\sqrt{\frac{693\times 7}{2\times 22}}=21cm $ Again, according to the question, $ 2\pi r _2-2\pi r _1=22 $

$ \Rightarrow $ $ \pi \times 21-2\pi r _1=22 $

$ \Rightarrow $ $ \frac{22}{7}\times 21-2\pi r _1=22 $

$ \Rightarrow $ $ 66-2\pi r _1=22 $

$ \Rightarrow $ $ 2\pi r _1=44 $
$ \Rightarrow $ $ 2\times \frac{22}{7}\times r _1=44 $ $ r _1=7cm $

$ \therefore $ $ d _1=14cm $

$ \therefore $ $ d _1+d _2=14+21=35cm $

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