Question : The value of $\frac{6.35 \times 6.35 \times 6.35+3.65 \times 3.65 \times 3.65}{63.5 \times 63.5+36.5 \times 36.5-63.5 \times 36.5}$ is equal to:
Option 1: 0.1
Option 2: 10
Option 3: 1
Option 4: 0.01
Correct Answer: 0.1
Solution :
$\frac{6.35 \times 6.35 \times 6.35+3.65 \times 3.65 \times 3.65}{63.5 \times 63.5+36.5 \times 36.5-63.5 \times 36.5}$
= $\frac{(6.35 \times 6.35+3.65 \times 3.65-6.35 \times 3.65)(6.35+3.65)}{(6.35 \times 6.35+3.65 \times 3.65-6.35 \times 3.65)(10 \times 10)}$
= $\frac{6.35+3.65}{100}$
= $\frac{1}{10}$
= 0.1
Hence, the correct answer is 0.1.
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