Question : The value of $\frac{27 \times(0.25)^3+125(0.05)^3}{(0.75)^2-0.25 \times 0.5}$ is :
Option 1: 1
Option 2: 0.75
Option 3: 0.25
Option 4: 0.5
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Correct Answer: 1
Solution :
Given expression,
$\frac{27 \times(0.25)^3+125(0.05)^3}{(0.75)^2-0.25 \times 0.5}$
= $\frac{27×(0.25)^3+(5×0.05)^3}{(0.75)^2−0.25×0.5}$
= $\frac{27×(0.25)^3+(0.25)^3}{(0.25×3)^2−0.25×0.5}$
= $\frac{(0.25)^3×(27+1)}{(0.25)^2×9−0.25×0.5}$
= $\frac{(0.25)^3×(28)}{(0.25)×[(9×0.25)−0.5]}$
= $\frac{(0.25)^3×(28)}{(0.25)×[2.25−0.5]}$
= $\frac{0.25×0.25×28}{1.75}$
= $\frac{0.25×28}{7}$
= 1
Hence, the correct answer is 1.
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