Question : The value of $\frac{0.325 \times 0.325+0.175 \times 0.175-25 \times 0.00455}{5 \times 0.0065 \times 3.25-7 \times 0.175 \times 0.025}$ lies between:
Option 1: 0.35 and 0.45
Option 2: 0.15 and 0.25
Option 3: 0.25 and 0.35
Option 4: 0.05 and 0.15
Correct Answer: 0.25 and 0.35
Solution :
Given:
$\frac{0.325 \times 0.325+0.175 \times 0.175-25 \times 0.00455}{5 \times 0.0065 \times 3.25-7 \times 0.175 \times 0.025}$
$=\frac{0.325 \times 0.325+0.175 \times 0.175-2 \times 0.325\times0.175}{(0.325)^2- (0.175)^2 }$
$=\frac{(0.325 -0.175)^2}{(0.325+0.175)(0.325-0.175) }$
$=\frac{(0.325 -0.175)}{(0.325+0.175) }$
$=0.3$
Hence, the correct answer is 0.25 and 0.35.
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