Question : The average weight of a class of 30 students is 45 kg. One of the students whose weight is 48.5 kg was replaced by another student and the average weight was increased by 200 g. Find the weight of the new student.
Option 1: 54.5 kg
Option 2: 50 kg
Option 3: 55 kg
Option 4: 51 kg
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Correct Answer: 54.5 kg
Solution : Total weight of students initially $= 30 \times 45 = 1350$ kg Total weight after the student left $= 1350-48.5 = 1301.5$ kg Let the weight of the new student be $x$. According to the problem, $\frac{1301.5+x}{30} = 45+\frac{200}{1000}$ $⇒\frac{1301.5+x}{30} = 45+0.2$ $⇒1301.5+x = 45.2\times 30$ $⇒1301.5+x= 1356$ $\therefore x = 1356-1301.5 = 54.5$ kg Hence, the correct answer is 54.5 kg.
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