Question : The average weight of the first 11 people among 12 people is 95 kg. The weight of the 12th person is 33 kg more than the average weight of all 12 people. The weight of the 12th person is:
Option 1: 128.75 kg
Option 2: 128 kg
Option 3: 131 kg
Option 4: 97.45 kg
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Correct Answer: 131 kg
Solution :
Let the average weight of the 12 people be $x$.
Then, the weight of the 12th person is $(x+33)$.
Total weight of all 12 people = $(11×95) + x +33$
Average weight of all 12 people = $\frac{(11×95)+x+33}{12}$
It is given that:
⇒ $x =\frac{(11×95)+x+33}{12}$
⇒ $x =\frac{1045+x+33}{12}$
⇒ $x =\frac{1078+x}{12}$
⇒ $12x=1078+x$
⇒ $11x=1078$
⇒ $x=\frac{1078}{11}$
$\therefore x=98$
$\therefore$ The weight of the 12
th
person is = 98 + 33 = 131 kg
Hence, the correct answer is 131 kg.
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