Question : The value of $\frac{0.325 \times 0.325+0.175 \times 0.175+25 \times 0.00455}{5 \times 0.0065 \times 3.25-7 \times 0.175 \times 0.025}-\frac{0.5}{1.5}$ is:
Option 1: –3
Option 2: 3
Option 3: –1
Option 4: 0
Correct Answer: 3
Solution :
$\frac{0.325 \times 0.325+0.175 \times 0.175+25 \times 0.00455}{5 \times 0.0065 \times 3.25-7 \times 0.175 \times 0.025}-\frac{0.5}{1.5}$
$=\frac{0.325^2+0.175^2+2 \times 0.325 \times0.175}{0.325^2-0.175^2}-\frac{0.5}{1.5}$
$=\frac{(0.325+0.175)^2}{(0.325+0.175)(0.325-0.175)}-\frac{0.5}{1.5}$
$=\frac{(0.325+0.175)}{(0.325-0.175)}-\frac{0.5}{1.5}$
$=\frac{(0.5)}{(0.15)}-\frac{0.5}{1.5}$
$=\frac{10}{3}-\frac{1}{3}$
$=3$
Hence, the correct answer is 3.
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