Question
Download Solution PDFIn a class, the number of boys is 40% more than that of girls. In and examination, the average marks obtained by boys is 20% less than the average marks obtained by girls. If the average marks obtained by all the boys and girls is 53, then what is the average marks obtained by the boys ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Number of boys is 40% more than that of girls.
Average marks obtained by boys is 20% less than the average marks obtained by girls.
Average marks obtained by all the boys and girls (overall average) = 53.
Calculation:
Let the number of girls be G.
Number of boys (B) = G + 40% of G = G + 0.40G = 1.4G
Let the average marks obtained by girls be Mg.
Average marks obtained by boys (Mb) = Mg - 20% of Mg = Mg - 0.20Mg = 0.8Mg
The total marks for boys = Number of boys × Average marks of boys = B × Mb
The total marks for girls = Number of girls × Average marks of girls = G × Mg
Overall average marks = (Total marks of boys + Total marks of girls) / (Total number of boys + Total number of girls)
53 = (B × Mb + G × Mg) / (B + G)
Substitute B = 1.4G and Mb = 0.8Mg into the overall average equation:
53 = (1.4G × 0.8Mg + G × Mg) / (1.4G + G)
53 = (1.12GMg + GMg) / (2.4G)
53 = GMg (1.12 + 1) / (2.4G)
53 = Mg (2.12) / 2.4
Mg = (53 × 2.4) / 2.12
Mg = 127.2 / 2.12 = 60
The average marks obtained by girls (Mg) = 60.
Average marks obtained by the boys (Mb):
Mb = 0.8Mg
Mb = 0.8 × 60
Mb = 48
∴ The correct answer is option 2.
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