Question : If A = $\frac{1}{7}$ and B = $\frac{1}{8}$ and the average of A, B and C is $\frac{1}{13}$, then the value of C is:
Option 1: $-\frac{31}{728}$
Option 2: $-\frac{27}{728}$
Option 3: $-\frac{89}{728}$
Option 4: $-\frac{49}{728}$
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Correct Answer: $-\frac{27}{728}$
Solution :
Given:
A = $\frac{1}{7}$ and B = $\frac{1}{8}$
The average of A, B, and C = $\frac{1}{13}$
Total of A, B, and C = $\frac{1}{13}×3=\frac{3}{13}$
C = $\frac{3}{13}-(\frac{1}{7}+\frac{1}{8})$
⇒ C = $\frac{3}{13}-\frac{15}{56}$
$\therefore$ C = $-\frac{27}{728}$
Hence, the correct answer is $-\frac{27}{728}$.
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