Question

Evaluate (using formulae) $\frac{0.3\times 0.3\times 0.3+0.1\times 0.1\times 0.1}{0.3\times 0.3-0.3\times 0.1+0.1\times 0.1}$

• A. $0.5$
• B. $0.4$
• C. $0.3$
• D. $0.2$

Answer 1

The correct option is B $0.4$

Given,
$\frac{0.3\times 0.3\times 0.3+0.1\times 0.1\times 0.1}{0.3\times 0.3-0.3\times 0.1+0.1\times 0.1}$

$\Rightarrow \frac{(0.3{)}^3+(0.1{)}^3}{(0.3{)}^2-0.3\times 0.1+(0.1{)}^2}$

$\Rightarrow \frac{(0.3+0.1)\left(\right(0.3{)}^2-0.3\times 0.1+\left(0.1{)}^2\right)}{(0.3{)}^2-0.3\times 0.1+(0.1{)}^2}$ [$a^3+b^3=(a+b)(a^2-ab+b^2)$]

$\Rightarrow 0.3+0.1=0.4$

Option B is correct.