SSC CHSL 10 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

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Question : 53 of 100

Marks: +1, -0

If

x+\;{1}/{15 x}=3

, then the value of

9 x^{3}+\;{1}/{375 x^{3}}

will be

$237.6$
$376.2$
$273.6$
$367.2$

Solution:

Given,

x+\;{1}/{15 x}=3

Take cube on both sides,

∴ (x+\;{1}/{15 x})^{3}=(x)^{3}+(\;{1}/{15 x})^{3}

\;\; +3 × x × \;{1}/{15 x} ×(x+\;{1}/{15 x})

⇒ \;\; [ ∵ (a+b)^{3}=(a^{3}+b^{3})+3 a b(a+b)]

⇒ \;\; (3)^{3}=x^{3}+\;{1}/{3375 x^{3}}+\;{1}/{5} × 3

⇒ x^{3}+\;{1}/{3375 x^{3}} \;\; =27-\;{3}/{5}=\;{135-3}/{5}

\;\; =26.4

Multiply by 9 on both sides, we get

\;9 x^{3}+\;{9 × 1}/{3375 x^{3}}=9 × 26.4

∴ \;9 x^{3}+\;{1}/{375 x^{3}}=237.6

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