Question : The value of $\frac{1}{4}+\frac{\left[(20.35)^2-(8.35)^2\right] \times 0.0175}{(1.05)^2+(1.05)(27.65)}$ is:
Option 1: $\frac{9}{20}$
Option 2: $\frac{7}{20}$
Option 3: $\frac{3}{20}$
Option 4: $\frac{3}{10}$
Correct Answer: $\frac{9}{20}$
Solution :
$\frac{1}{4}+\frac{\left[(20.35)^2-(8.35)^2\right] \times 0.0175}{(1.05)^2+(1.05)(27.65)}$
$=\frac{1}{4}+\frac{\left[(20.35+8.35)(20.35-8.35)\right] \times 0.0175}{(1.05)[1.05+27.65]}$
$=\frac{1}{4}+\frac{\left[(12)(28.70)\right] \times 0.0175}{(1.05)[28.70]}$
$=\frac{1}{4}+\frac{12 \times 0.0175}{(1.05)}$
$=\frac{1}{4}+\frac{1}{5}$
$=\frac{9}{20}$
Hence, the correct answer is $\frac{9}{20}$.
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