Question : The average weight of A, B, C and D is 33 kg. C is 12 kg lighter than A, while B is 6 kg heavier than C. D's weight is 10 kg less than that of C. What is the average weight of A and D?
Option 1: 34 kg
Option 2: 33 kg
Option 3: 35 kg
Option 4: 32 kg
Correct Answer: 32 kg
Solution :
Average weight of A, B, C, and D = 33 kg
C is 12 kg lighter than A.
B is 6 kg heavier than C.
D is 10 kg less than that of C.
Let the value of A be $x$ kg.
Weight of C $= x - 12$ kg
Weight of B $= x - 12 + 6 = x - 6$ kg
Weight of D $= x -12 - 10 = x - 22$ kg
Average = $\frac{\text{Sum of values}}{\text{Number of values}}$
So, the average of A, B, C, and D $= \frac{x+x-12+x-6+x-22}{4} = \frac{4\text{x}-40}{4} = x -10$
Now, $x - 10 = 33$
⇒ $x = 33 + 10 = 43$ kg
Then, the weight of A = 43 kg
Weight of D $= x - 22 = 43 - 22 = 21$ kg
So, the average weight of A and D $= \frac{43+21}{2} = \frac{64}{2} = 32$ kg
$\therefore$ The average weight of A and D is 32 kg.
Hence, the correct answer is 32 kg.
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