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SSC CPO 2022 PYQ — Question 148

SSC CPO - 9 Nov 2022 - Shift 1 • Quantitative Aptitude • Q148

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If a−1a−5=10,a - \frac {1}{a-5} = 10, then the value of (a−5)3−1(a−5)3(a-5)^3-\frac {1}{(a-5)^3} is:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 140.

Given that

 If a−1a−5=10,a - \frac {1}{a-5} = 10, 

(a - 5) - 1/(a - 5) = 5

Let x = a - 5

So, x - 1/x = 5

Formula used

x3 - 1/x3 = (x - 1/x)3  + 3 (x - 1/x)

Calculation

x3 - 1/x3 = (5)3  + 3 × 5 = 125 + 15 = 140

Hence, (a−5)3−1(a−5)3(a-5)^3-\frac {1}{(a-5)^3} = 140