Question : What is the value of $\frac{\frac{1}{2} \times \frac{1}{24} \div \frac{1}{36}+\frac{1}{48}-\frac{1}{60}}{\frac{1}{12}+\frac{1}{24}+\frac{1}{36} \times \frac{1}{6}} ?$
Option 1: $\frac{1841}{119}$
Option 2: $\frac{1629}{280}$
Option 3: $\frac{1131}{124}$
Option 4: $\frac{733}{145}$
Correct Answer: $\frac{1629}{280}$
Solution :
Given: $\frac{\frac{1}{2} \times \frac{1}{24} \div \frac{1}{36}+\frac{1}{48}-\frac{1}{60}}{\frac{1}{12}+\frac{1}{24}+\frac{1}{36} \times \frac{1}{6}}$
= $\frac{\frac{1}{2} \times \frac{1}{24} \times \frac{36}{1}+\frac{1}{48}-\frac{1}{60}}{\frac{1}{12}+\frac{1}{24}+\frac{1}{36} \times \frac{1}{6}}$
= $\frac{\frac{3}{4}+\frac{1}{48}-\frac{1}{60}}{\frac{1}{12}+\frac{1}{24}+ \frac{1}{216}}$
= $\frac{\frac{180+5-4}{240}}{\frac{18+9+1}{216}}$
= $\frac{\frac{181}{240}}{\frac{28}{216}}$
= $\frac{181}{240}\times\frac{216}{28}$
= $\frac{1629}{280}$
Hence, the correct answer is $\frac{1629}{280}$.
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