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SSC CHSL 2023 PYQ — Question 65

SSC CHSL 2023 - 04 Aug 2023 - Shift 2 • Quantitative Aptitude • Q65

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If ab=83−ba \sqrt{\frac{a}{b}}=\frac{8}{3}- \sqrt{\frac{b}{a}} and a - b = 10, then the value of ab is:

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Correct answer: A

Explanation

The correct answer is option 1 i.e.  3217\frac{1}{7}.

We have given,ab=83−ba \sqrt{\frac{a}{b}}=\frac{8}{3}- \sqrt{\frac{b}{a}}

and a - b = 10

⇒ (a - b)2 = a2 + b2 - 2ab

⇒ 100 + 2ab =  a2 + b2 .............1

ab=83−ba \sqrt{\frac{a}{b}}=\frac{8}{3}- \sqrt{\frac{b}{a}}

⇒ ab+ba=83 \sqrt{\frac{a}{b}}+ \sqrt{\frac{b}{a}}=\frac{8}{3}

Square on both sides

⇒ ab+ba+2=649\frac{a}{b}+\frac{b}{a} + 2= \frac{64}{9}

⇒  a2+b2ab=649−2\frac{a^2+b^2}{ab} =\frac{64}{9}-2

 ⇒  a2+b2ab=469\frac{a^2+b^2}{ab} =\frac{46}{9}

Put the value of a2 + b2 from equation 1

100+2abab=469\frac{100+2ab}{ab} =\frac{46}{9}

⇒  900 + 18ab = 46ab

⇒ ab = 900/28

⇒ ab = 225/7 = 3217\frac{1}{7}