SarkariPYQ

SSC CPO 2020 PYQ — Question 132

SSC CPO - 25 Nov 2020 - Shift 2 • Quantitative Aptitude • Q132

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The value of 427×427×427+325×325×32542.7×42.7+32.5×32.5−42.7×32.5\frac{427 \times 427 \times 427 + 325 \times 325 \times 325}{42.7 \times 42.7 + 32.5 \times 32.5 - 42.7 \times 32.5 } is :

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 75200.

⇒ 427×427×427+325×325×32542.7×42.7+32.5×32.5−42.7×32.5\frac{427 \times 427 \times 427 + 325 \times 325 \times 325}{42.7 \times 42.7 + 32.5 \times 32.5 - 42.7 \times 32.5 }

⇒ (427)3+(325)3(42.7)2+(32.5)2−42.7×32.5\frac{(427)^3 + (325)^3}{(42.7)^2 + (32.5)^2 - 42.7 \times 32.5 }

We know that

⇒ a3 + b3 = (a + b)(a2 + b2 - ab)

⇒ (427+325)((427)2+(325)2−427×325)×100(42.7)2+(32.5)2−42.7×32.5\frac{(427+325)((427)^2 + (325)^2 - 427\times325)\times100}{(42.7)^2 + (32.5)^2 - 42.7 \times 32.5 }

⇒​​​​​​​ (427 + 325) × 100 = 75200

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