# The mean weight of 100 students in a class is 46 kg. The mean weight of boys is 50 kg and that of girls is 40 kg. The number of boys exceeds the numbe

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The mean weight of 100 students in a class is 46 kg. The mean weight of boys is 50 kg and that of girls is 40 kg. The number of boys exceeds the number of girls by
1. 10
2. 15
3. 20
4. 25

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Correct Answer - Option 3 : 20

Given:

The mean weight of 100 students is 46 kg

The mean weight of boys is 50 kg

The mean weight of girls is 40 kg

Formula used:

Mean = Sum of total observations/Number of observations

Calculations:

Let the number of boys and girls be x and (100 - x)

According to the question, we have

Mean = {50x + 40(100 - x)}/100

⇒ 46 = {50x + 40(100 - x)}/100

⇒ 4600 = 50x + 4000 - 40x

⇒ 4600 - 4000 = 10x

⇒ x = 600/10

⇒ x = 60

So, The number of boys is 60

Hence, The number of girls is

Number of girls = 100 - x

⇒ Number of girls = 100 - 60

⇒ Number of girls = 40

The number of boys exceeds that the number of girls by

⇒ Difference = 60 - 40

⇒ Difference = 20

∴ The number of boys exceeds that the number of girls by 20.