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SSC CPO 2020 PYQ — Question 128

SSC CPO - 25 Nov 2020 - Shift 1 • Quantitative Aptitude • Q128

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The value of 5.35×5.35×5.35+3.65×3.65×3.6553.5×53.5+36.5×36.5−53.5×36.5\frac{5.35 \times 5.35 \times 5.35 + 3.65 \times 3.65 \times 3.65}{53.5 \times 53.5 + 36.5 \times 36.5 - 53.5 \times 36.5} is :

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Correct answer: C

Explanation

The correct answer is Option 3 i.e 0.09.

⇒ 5.35×5.35×5.35+3.65×3.65×3.6553.5×53.5+36.5×36.5−53.5×36.5\frac{5.35 \times 5.35 \times 5.35 + 3.65 \times 3.65 \times 3.65}{53.5 \times 53.5 + 36.5 \times 36.5 - 53.5 \times 36.5}

⇒ (5.35)3+(3.65)3(53.5)2+(36.5)2−53.5×36.5\frac{(5.35)^3+ (3.65)^3}{(53.5)^2 + (36.5)^2 - 53.5 \times 36.5}

We know that

a3 + b3 = (a2 – ab + b2)(a + b)

Applying the given question

⇒ ((5.35)2+(3.65)2−5.35×3.65)(5.35+3.65)(53.5)2+(36.5)2−53.5×36.5\frac{((5.35)^2+ (3.65)^2 - 5.35 \times 3.65)(5.35 + 3.65)}{(53.5)^2 + (36.5)^2 - 53.5 \times 36.5}

⇒ ((5.35)2+(3.65)2−5.35×3.65)(5.35+3.65)100×[(5.35)2+(3.65)2−5.35×3.65]\frac{((5.35)^2+ (3.65)^2 - 5.35 \times 3.65)(5.35 + 3.65)}{100\times[(5.35)^2 + (3.65)^2 - 5.35 \times 3.65]}

⇒ (5.35+3.65)100\frac{(5.35 + 3.65)}{100}

⇒ 91009\over100 = 0.09