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# The average weight of 8 boys is 57 Kg, if weight of 7 of them are 64, 42, 29, 39, 80, 52 and 55 kgs, then the weight of the ${8^{th}}$ student isA.75B.95C.55D.35

Last updated date: 20th Jun 2024
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Hint: We will use the formula for average to calculate the total weight of the 8 boys. We will calculate the sum of weights of the 7 boys. The weight of the ${8^{th}}$ boy will be the difference between the total weight and the sum of weights of the 7 boys. We will subtract the 2 quantities to obtain the weight of the ${8^{th}}$ boy.

Formulas used:
The formula for the average weight of $n$ people:
Average Weight $=$ Total weight of $n$ people $\div n$.
We know that the average weight of 8 boys is 57 Kg. We will substitute 57 for average weight and 8 for $n$ in the formula for the average weight:
$\Rightarrow 57 =$Total weight of 8 people $\div 8$
On cross multiplying 8 with 57, we get
$\Rightarrow 57 \times 8 =$Total weight of 8 people
$\Rightarrow 45{\rm{6}} =$ Total weight of 8 people
We have calculated that the total weight of 8 people is 456 Kg. Out of the 8 people, we know the weight of 7 people. We will assume that the weight of the ${8^{th}}$ boy is $x$ kg. So, the total weight of 8 people will be:
$x + 64 + 42 + 29 + 39 + 80 + 52 + 55$
We know that the total weight is 465 Kg. On equating the above expression with 465, we get
$\Rightarrow 456 = x + 64 + 42 + 29 + 39 + 80 + 52 + 55$
Adding the like terms, we get
$\Rightarrow 456 = x + 361$
Subtracting 361 from both sides, we get
$\Rightarrow 456 - 361 = x + 361 - 361$
$\Rightarrow 95 = x$
We can conclude that the weight of the ${8^{th}}$ student is 95 Kg.
$\therefore$ Option B is the correct option.

Note: The average which is also known as the arithmetic mean is often used as the representative of a large number of quantities. It is assumed to be the central value of the data. Here the weight is given in Kg so we need to keep the weight in the same unit and not change it throughout.