Question : Ram, Shyam, Rohan, Reeta, and Mukesh are five members of a family who are weighed consecutively and their average weight is calculated after each member is weighed. If the average weight increases by 2 kg each time, how much heavier is Mukesh than Ram?
Option 1: 14 kg
Option 2: 18 kg
Option 3: 16 kg
Option 4: 12 kg
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Correct Answer: 16 kg
Solution :
Let the weight of Ram be $x$ kg.
Average weight $= x$ kg
According to the question,
After adding Shyam, the average weight $= (x + 2)$ kg
Weight of Shyam $= 2(x + 2) - x = (x + 4)$ kg
After adding Rohan, the average weight $= (x + 4)$ kg
Weight of Rohan $= 3(x + 4) - x - (x + 4) = (x + 8)$ kg
After adding Reeta, the average weight $= (x + 6)$ kg
Weight of Reeta $= 4(x + 6) - x - (x + 4) - (x + 8) = (x + 12)$ kg
After adding Mukesh, the average weight = $(x + 8)$ kg
Weight of Mukesh $= 5(x + 8) - x- (x + 4) - (x + 8) - (x + 12) = (x + 16)$ kg
Now, Mukesh is heavier than Ram by $= (x + 16) - x =$ 16 kg
Hence, the correct answer is 16 kg.
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