Q52
ArithmeticAverages & Ages
The average marks obtained by the boys and girls in a class are 52 and 42 respectively. If the average marks of all students in that class is 50, then the percentage of boys present in the class is
- a.40%
- b.50%
- c.80%
- d.Can't be determined from above data.
Answer: (C) 80%
Use alligation on the averages: boys 52, girls 42, combined 50. Boys : girls $= (50 - 42) : (52 - 50) = 8 : 2 = 4 : 1$, so boys are $\frac{4}{5} = 80\%$ of the class. Algebra gives the same result: if $b$ is the fraction of boys, $52b + 42(1 - b) = 50$, so $b = 0.8$. Option D is the trap, since the actual numbers are not needed; a ratio is enough to give a percentage. Common-sense check: the combined average (50) lies much closer to the boys' average, so boys must be the large majority.