The mean weight of 150 students in a certain class is 60 kilograms. The mean dweight of boys in the class is 70 kilograms and that of the girls is 55 kilograms, then the number of boys and girls are (A) 100, 50 (B) 50, 100 (C) 75, 75 (D) 60, 90

Given

Total students in class=150

Mean weight = 60 kg

Total weight = 150 x 60 = 9000 kg

Consider the total number of boys = x

Mean weight of boys = 70 kg

Total weight of boys = 70 ✕ x = 70x kg

Total number of girls = Total students – number of boys = 150 – x

Mean weight of girls = 55 kg

Total weight of girls = 55 ✕ (150 – x) = 55 ✕ 150 – 55x = (8250 – 55x) kg

Total weight = weight of boys + weight of girls

9000 = 70x + (8250 – 55x)

9000 = 70x + 8250 – 55x

9000 – 8250 = 70x – 55x

750 = 15x

x = 750/15

We get,

x = 50

So, number of boys = 50

Number of girls = 150 – 50 = 100

Therefore, the correct option is (B)

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