Question : The value of $\frac{(0.67 \:\times\: 0.67 \:\times\: 0.67)\:-\:(0.33 \:\times\: 0.33 \:\times\: 0.33)}{(0.67 \:\times\: 0.67)\:+\:(0.67 \:\times\: 0.33)\:+\: (0.33 \:\times\: 0.33)}$ is:
Option 1: 11
Option 2: 1.1
Option 3: 3.4
Option 4: 0.34
Correct Answer: 0.34
Solution :
$\frac{(0.67 \:\times\: 0.67 \:\times\: 0.67)\:-\:(0.33 \:\times\: 0.33 \:\times\: 0.33)}{(0.67 \:\times\: 0.67)\:+\:(0.67 \:\times\: 0.33)\:+\: (0.33 \:\times\: 0.33)}$
= $\frac{(0.67^{3}\:-\:0.33^{3})}{0.67^{2}\:+\:(0.67 \:\times\: 0.33)\:+\:0.33^{2}}$
= $\frac{(0.67\:-\:0.33)({0.67^{2}\:+\:(0.67 \:\times\: 0.33)\:+\:0.33^{2}})}{0.67^{2}\:+\:(0.67 \:\times\: 0.33) \:+\: 0.33^{2}}$
= $0.67 - 0.33$
= $0.34$
Hence, the correct answer is 0.34.
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