The value of $$\frac{{27 \times {{\left( {0.25} \right)}^3} + 125{{\left( {0.05} \right)}^3}}}{{{{\left( {0.75} \right)}^2} - 0.25 \times 0.5}}$$ is:
A. 1
B. 0.75
C. 0.25
D. 0.5
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & \frac{{27 \times {{\left( {0.25} \right)}^3} + 125{{\left( {0.05} \right)}^3}}}{{{{\left( {0.75} \right)}^2} - 0.25 \times 0.5}} \cr & = \frac{{\frac{{27 \times 25 \times 25 \times 25}}{{1000000}} + \frac{{125 \times 5 \times 5 \times 5}}{{1000000}}}}{{\frac{{75 \times 75}}{{10000}} - \frac{{25 \times 5}}{{1000}}}} \cr & = \frac{{\frac{{27 \times 25 \times 25 \times 25}}{{1000}} + \frac{{125 \times 5 \times 5 \times 5}}{{1000}}}}{{\frac{{75 \times 75 - 25 \times 5 \times 10}}{{10}}}} \cr & = \frac{{\frac{{27}}{8} + \frac{1}{8}}}{{\frac{{45 - 10}}{{10}}}} \cr & = \frac{{280}}{{8 \times 35}} \cr & = 1 \cr} $$Related Questions on Simplification
A. 20
B. 80
C. 100
D. 200
E. None of these
A. Rs. 3500
B. Rs. 3750
C. Rs. 3840
D. Rs. 3900
E. None of these
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