In a class, the number of boys is 40% more than that of girls. In an 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 ?

Correct option is A

​$$\textbf{Given:} \\\text{Number of boys is } 40\% \text{ more than girls} \\\text{Average marks of boys is } 20\% \text{ less than girls} \\\text{Overall average marks} = 53 \\\textbf{Concept Used:} \\\text{Weighted average} \\\textbf{Formula Used:} \\\text{Overall Average} = \frac{\text{Total marks of boys + Total marks of girls}}{\text{Total students}} \\\textbf{Solution:} \\\text{Let number of girls} = 100 \\\text{Then number of boys} = 140 \\\text{Let average marks of girls} = x \\\text{Average marks of boys} = 80\% \text{ of } x = 0.8x \\\text{Total marks of girls} = 100x \\\text{Total marks of boys} = 140 \times 0.8x = 112x \\\text{Total students} = 100 + 140 = 240 \\\text{Overall average:} \\\frac{100x + 112x}{240} = 53 \\\frac{212x}{240} = 53 \\212x = 12720 \\x = 60 \\\text{Average marks of boys} = 0.8x \\= 0.8 \times 60 \\= 48 \\\textbf{Final Answer:} \\48$$​​