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: 0
Option 3: $\frac{7}{3}$
Option 4: $\frac{11}{3}$
Correct Answer: $\frac{11}{3}$
Solution :
Given: $\frac{0.325 \times 0.325+0.175 \times 0.175+25 \times 0.00455}{5 \times 0.0065 \times 3.25-7 \times 0.175 \times 0.025}+\frac{0.5}{1.5}$
$=\frac{(0.325)^2 \times(0.175)^2+2 \times 0.0325\times0.175}{0.0325\times3.25- 0.225 \times 1.025}+\frac{0.5}{1.5}$
$=\frac{(0.325+0.175)^2}{0.325\times0.325- 0.175 \times0.175}+\frac{0.5}{1.5}$
$=\frac{(0.325+0.175)^2}{(0.325)^2(0.175)^2}+\frac{0.5}{1.5}$
$=\frac{(0.325+0.175)^2}{(0.325+0.175)(0.325-0.175)}+\frac{0.5}{1.5}$
$=\frac{(0.325+0.175)}{(0.325-0.175)}+\frac{0.5}{1.5}$
$=\frac{0.5}{0.15}+\frac{0.5}{1.5}$
$=\frac{5+0.5}{1.5}$
$=\frac{5.5}{1.5}$
$=\frac{11}{3}$
Hence, the correct answer is $\frac{11}{3}$.
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