Question : If A is $\frac{1}{6}$th of C, and B is twice of A, and the average of A, B, and C is 30, then the difference between A and C is:
Option 1: 40
Option 2: 60
Option 3: 50
Option 4: 80
Correct Answer: 50
Solution :
According to the question,
$A = \frac{1}{6}C$
$B = 2A=\frac{C}{3}$
Average of $n$ observations $=\frac{\text{Sum of all observations}}{n}$
Average $=\frac{A+B+C}{3} = \frac{\frac{C}{6} +\frac{C}{3} +C}{3}$
$⇒ 30 = \frac{\frac{9C}{6}}{3}$
$⇒ 30 = \frac{C}{2}$
$\therefore C = 60$
Also,
⇒ $A = \frac{1}{6}C = \frac{1}{6}× 60 = 10$
$\therefore$ C – A = 60 – 10 = 50
Hence, the correct answer is 50.
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