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SSC CHSL 2023 PYQ — Question 73

SSC CHSL - 07 Aug 2023 - Shift 4 • Quantitative Aptitude • Q73

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Simplify the following expression:(0.96×0.96×0.96+0.04×0.04×0.04)(0.96×0.96−0.96×0.04+0.04×0.04)(0.96\times0.96\times0.96+0.04\times0.04\times0.04)\over(0.96\times0.96-0.96\times0.04+0.04\times0.04)

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 1.

(0.96×0.96×0.96+0.04×0.04×0.04)(0.96×0.96−0.96×0.04+0.04×0.04)(0.96\times0.96\times0.96+0.04\times0.04\times0.04)\over(0.96\times0.96-0.96\times0.04+0.04\times0.04)

⇒ (0.963+0.043)(0.96×0.96−0.96×0.04+0.04×0.04)(0.96^3+0.04^3)\over(0.96\times0.96-0.96\times0.04+0.04\times0.04)

We know that,

a3 + b3 = (a + b)(a2 + b2 - ab)

So,

⇒ (0.96+0.04)(0.96×0.96−0.96×0.04+0.04×0.04)(0.96×0.96−0.96×0.04+0.04×0.04)(0.96+0.04)(0.96\times0.96-0.96\times0.04+0.04\times0.04)\over(0.96\times0.96-0.96\times0.04+0.04\times0.04)

⇒​​​​​​​ 0.96 + 0.04 = 1