Question : In a class, there are 54 students. $33 \frac{1}{3}$% of the number of students are boys and the rest are girls. The average score in mathematics of boys is 50% more than that of girls. If the average score of all the students is 70, then what is the average score of the boys?
Option 1: 81
Option 2: 84
Option 3: 87
Option 4: 90
Correct Answer: 90
Solution :
A class of 54 students.
Average score in mathematics of boys = 50% more than that of girls
Average = $\frac{\text{Sum of values}}{\text{No. of values}}$
Total number of students = 54
$33\frac{1}{3}$% = \(\frac{100}{3}\)%= $\frac{1}{3}$
Number of boys = 54 × $\frac{1}{3}$= 18
Number of girls = 54 – 18 = 36
Let the average score of girls = $2x$
So, the average score of boys $=2x × (\frac{3}{2}) = 3x$
According to the question,
$18 × 3x + 36 × 2x = 54 × 70$
⇒ $54x + 72x = 3780$
⇒ $126x = 3780$
⇒ $x = \frac{3780}{126} = 30$
Average score of boys = 30 × 3 = 90
Hence, the correct answer is 90.
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