Question : Find the value of $k$, if $13 - [10 - \{16 + 8 \div(k - 2)\} + 2] = 20$
Option 1: $\frac{14}{3}$
Option 2: $\frac{31}{3}$
Option 3: $\frac{40}{13}$
Option 4: $\frac{23}{13}$
Correct Answer: $\frac{14}{3}$
Solution :
$13-[10-\{16+8 \div(k-2)\}+2] = 20$
⇒ $13-[10-{16-\frac{8}{k-2}}+2] = 20$
⇒ $13-[10-\{\frac{16k-32+8}{k-2}\}+2] = 20$
⇒ $13-[\frac{10k-20-16k+32-8+2k-4}{k-2}]=20$
⇒ $13-[\frac{-4k}{k–2}] = 20$
⇒ $13+\frac{4k}{k–2} = 20$
⇒ $13k-26+4k = 20k-40$
⇒ $3k = 14$
⇒ $k = \frac{14}{3}$
Hence, the correct answer is $\frac{14}{3}$.
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