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Question : The value of $9 \div\left\{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} \div\left(\frac{3}{4}-\frac{1}{3}\right)\right.$ of $\left.\frac{2}{9}\right\}$ is:

Option 1: $\frac{540}{173}$

Option 2: $\frac{340}{173}$

Option 3: $\frac{480}{173}$

Option 4: $\frac{2540}{173}$


Team Careers360 13th Jan, 2024
Answer (1)
Team Careers360 23rd Jan, 2024

Correct Answer: $\frac{540}{173}$


Solution : $9 \div\left\{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} \div\left(\frac{3}{4}-\frac{1}{3}\right)\right.$ of $\left.\frac{2}{9}\right\}$
$=9 \div\left\{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} \div\left(\frac{5}{12}\right)\right. \text{of}\left.\frac{2}{9}\right\}$
$=9 \div({\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} \div\frac{5}{54}})$
$=9 \div({\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} \times\frac{54}{5}})$
$=9 \div({\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{9}{5} })$
$=9 \div({\frac{30+20+15+108}{60}})$
$=9 \div({\frac{173}{60}})$
$=9 \times({\frac{60}{173}})$
$={\frac{540}{173}}$
Hence, the correct answer is ​​​​​​​${\frac{540}{173}}$.

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