SSC CPO 2020 PYQ — Question 118

The correct answer is option 3 i.e. 0.076.

Here $4.35 \times 4.35 \times 4.35 + 3.25\times 3.25\times 3.25 \over 43.5 \times 43.5 +32.5\times 32.5 -43.5\times32.5$can be written as $4.35 ^3+ 3.25^3\over 43.5^2+32.5^2-43.5\times32.5$

Now multiplying denominator and numerator by 10³ we get

⇒ $1\over10^3$ × $43.5 ^3+ 32.5^3\over 43.5^2+32.5^2-43.5\times32.5$ which is of the form $1\over10^3$  × $a^3+ b^3\over a^2+b^2-a\times b$

Now we know that a³ + b³ = (a + b)(a² + b² - a × b)

⇒ $1\over10^3$ × $(a+b)(a^2+b^2-a\times b)\over a^2+b^2-a\times b$

⇒ $1\over10^3$ × $(a+b)$

⇒ $1\over10^3$ × (43.5 + 32.5)

⇒ $1\over10^3$ × 76

⇒ 0.076