The mean weight of 150 students in a class is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. What is the number of boys in the class?
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A) 50 |
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B) 60 |
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C) 75 |
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D) 100 |
Correct Answer:
| A) 50 |
Given that, total number of students = 150 = \( \Large \left(n_{1}+n_{2}\right) \) and mean weight of 150 students = 60 kg. The mean weight of boys a1 = 70 kg and the mean weight of girls \( \Large a_{2} \) = 55 kg Let \( \Large n_{1} \) and \( \Large n_{2} \) be the number of boys and girl, respectively.
Therefore, \( \Large n_{1} + n_{2} \) = 150 ...(i)
\( \Large11 n_{1} + 11n_{2} \) = 1650 ...(ii)
Average weight = \( \Large \frac{n_{1}a_{1} + n_{2}a_{2}} {n_{1} + n_{2}} \)
=> \( \Large 60 = \frac{70n_{1} + 55n_{2}}{150} \)
=> \( \Large 70n_{1} + 55n_{2} \) = 9000
=> \( \Large 14n_{1} + 11n_{2} = 1800 \) .....(iii)
On subtracting Eq. (ii) from Eq. (iii). we get
\( \Large 3n_{1} = 150 => n_{1} = 50 \)
Hence, required number of boys is 50
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