Question : The average weight of A, B, and C is 65 kg. If the average weight of C and B is 61.5 kg, and the average weight of A and C is 68.5 kg, then the weight of C (in kg) is:
Option 1: 65
Option 2: 60
Option 3: 68
Option 4: 67
Correct Answer: 65
Solution :
Let the weights of A, B, and C as $a$, $b$, and $c$, respectively.
From the problem,
1. The average weight of A, B, and C is 65 kg.
$⇒\frac{a + b + c}{3} = 65$
$⇒a + b + c = 195$
2. The average weight of B and C is 61.5 kg.
$⇒\frac{b + c}{2} = 61.5$
$⇒b + c = 123$
3. The average weight of A and C is 68.5 kg.
$⇒\frac{a + c}{2} = 68.5$
$⇒a + c = 137$
Subtracting the second equation from the first,
$⇒a = 72$ kg
Substituting $a = 72$ kg into the third equation,
$⇒c = 137 - 72 = 65$ kg
Hence, the correct answer is 65.
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