Question : The value of 5 ÷ [5 + 8 – {4 + (4 of 2 ÷ 4) – (2 ÷ 4 of 2)}] is:
Option 1: $\frac{20}{23}$
Option 2: $\frac{5}{8}$
Option 3: $\frac{5}{7}$
Option 4: $\frac{20}{29}$
Correct Answer: $\frac{20}{29}$
Solution :
Given: 5 ÷ [5 + 8 – {4 + (4 of 2 ÷ 4) – (2 ÷ 4 of 2)}]
= $5 ÷ [5+8-\{{4+((4 \times 2) ÷ 4)-(2 ÷ (4 \times 2))}\}]$
= $5 ÷ [5+8-\{{4+(8 ÷ 4)-(2 ÷ 8)}\}]$
= $5 ÷ [5+8-\{{4+\frac{8}{4}-\frac{2}{8}}\}]$
= $5 ÷ [5+8-\{{4+2-\frac{1}{4}}\}] $
= $5 ÷ [5+8-\{{6-\frac{1}{4}}\}]$
= $5 ÷ [13-\frac{23}{4}]$
= $5 ÷\frac{29}{4}$
= $5\times\frac{4}{29}$
= $\frac{20}{29}$
Hence, the correct answer is $\frac{20}{29}$.
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