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The average weight of 40 students in a class is 75 kg. By mistake the weights of two students are read as 74 kg and 66 kg respectively instead of 66 kg and 54 kg. Find the corrected average weight of the class
- a)73.50 kg
- b)74.50 kg
- c)75.50 kg
- d)76.50 kg
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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The average weight of 40 students in a class is 75 kg. By mistake the ...
Answer – b) 74.50 kg Explanation : Weight of 40 students = 40*75 new weight = 40*75 – 74 – 66 + 66 + 54 = 40*75 – 20 so new average =( 40*75 – 20)/40 = 74.50 kg
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The average weight of 40 students in a class is 75 kg. By mistake the ...
To find the corrected average weight of the class, we need to first calculate the sum of the weights of all the students in the class.
Let's assume the sum of the weights of the 40 students is S.
The given average weight of the class is 75 kg, so we can write the equation:
S/40 = 75
Multiplying both sides of the equation by 40, we get:
S = 75 * 40
S = 3000 kg
Now, let's calculate the sum of the weights of the two students whose weights were read incorrectly.
Initially, their weights were read as 74 kg and 66 kg. However, the correct weights are 66 kg and 54 kg.
The sum of their incorrect weights is 74 + 66 = 140 kg.
The sum of their correct weights is 66 + 54 = 120 kg.
Therefore, the difference between the sum of the correct weights and the sum of the incorrect weights is:
140 - 120 = 20 kg.
To find the corrected sum of the weights, we need to subtract this difference from the initial sum of the weights.
Corrected sum of weights = S - difference = 3000 - 20 = 2980 kg.
Finally, we can calculate the corrected average weight of the class by dividing the corrected sum of weights by the number of students (40):
Corrected average weight = Corrected sum of weights / Number of students = 2980 / 40 = 74.50 kg.
Hence, the corrected average weight of the class is 74.50 kg, which matches option B.
Let's assume the sum of the weights of the 40 students is S.
The given average weight of the class is 75 kg, so we can write the equation:
S/40 = 75
Multiplying both sides of the equation by 40, we get:
S = 75 * 40
S = 3000 kg
Now, let's calculate the sum of the weights of the two students whose weights were read incorrectly.
Initially, their weights were read as 74 kg and 66 kg. However, the correct weights are 66 kg and 54 kg.
The sum of their incorrect weights is 74 + 66 = 140 kg.
The sum of their correct weights is 66 + 54 = 120 kg.
Therefore, the difference between the sum of the correct weights and the sum of the incorrect weights is:
140 - 120 = 20 kg.
To find the corrected sum of the weights, we need to subtract this difference from the initial sum of the weights.
Corrected sum of weights = S - difference = 3000 - 20 = 2980 kg.
Finally, we can calculate the corrected average weight of the class by dividing the corrected sum of weights by the number of students (40):
Corrected average weight = Corrected sum of weights / Number of students = 2980 / 40 = 74.50 kg.
Hence, the corrected average weight of the class is 74.50 kg, which matches option B.
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