Question

The value of the expression $\frac{10\times 10\times 10+5\times 5\times 5}{10\times 10-10\times 5+5\times 5}$ is :

• A. 15
• B. 10
• C. 5
• D. 20

Answer 1

The correct option is A 15

We have, $\frac{(10\times 10\times 10)+(5\times 5\times 5)}{(10\times 10)-(10\times 5)+5\times 5}$

$=\frac{{10}^3-5^3}{{10}^2-10\times 5+5^2}$

$=\frac{(10+5)({10}^2-10\times 5+5^2)}{({10}^2-10\times 5+5^2)}$ [Using the identity $(a^3+b^3)=(a+b)(a^2-ab+b^2)$]

$=(10+5)$ [On cancelling this term $({10}^2-10\times 5+5^2)$]

$=15$