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The mean weight of 100 students in a class is 46 kg. The mean weight of boys is 50 and of girls is 40 kg. Therefore, the number of boys is:
Answer & Solution
Correct Answer:
Option
B
Let number of boys are x and then number of girls
= (100 - x)
Thus,
50x + (100 - x) × 40 = 46 × 100
→ x = 60
Number of boys = 60
= (100 - x)
Thus,
50x + (100 - x) × 40 = 46 × 100
→ x = 60
Number of boys = 60
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LoginAccording to the given information, the mean weight of the 100 students is 46 kg. This means that the sum of the weights of all the students is equal to 46 multiplied by 100, which is 4600 kg.
We are also given that the mean weight of boys is 50 kg. So, the sum of the weights of all the boys is equal to 50 multiplied by 'x', which is 50x kg.
Similarly, the mean weight of girls is 40 kg. So, the sum of the weights of all the girls is equal to 40 multiplied by '100 - x', which is 40(100 - x) kg.
Since the total weight of all the students is equal to the sum of the weights of boys and girls, we can set up the following equation:
50x + 40(100 - x) = 4600
Simplifying the equation:
50x + 4000 - 40x = 4600
10x = 600
x = 60
Therefore, the number of boys in the class is 60.
The answer is B. 60.
Boys--------------Girls
50-----------------40
..............46..........
6--------------------4
6:4
Boys = 100*6/10 = 60
Girls = 40