The table below shows the drop-out rates, in percentage, at the Primary level (Classes I-V), the Elementary level (Classes I-VIII), and the Secondary level (Classes I-X) in India, separately for boys, girls, and the total, for the years 1996-97 to 2004-05. Gender bias is defined as the disproportion between the drop-out rate of boys and the drop-out rate of girls, at a given level.
Assume that every year, girls make up 55% of the students entering school, so boys make up 45%. Taking the number of students entering as the same fixed number each year, in which of the following years, as compared to the year before it, would the number of boys who reach secondary education be more than the number of girls who reach secondary education?
Show Hint
Work out the number of boys and girls who reach secondary level as a share of those entering, 45% boys and 55% girls, using each year's secondary drop-out rate, then compare the two.
Instead of plugging numbers into two separate expressions for boys and girls, it is quicker to reduce the condition to a single ratio test and compare that ratio against a fixed benchmark.
Boys entering are 45% of the cohort and girls are 55%, so for boys to end up more numerous than girls at secondary level we need $0.45(1-b/100) > 0.55(1-g/100)$, which rearranges to $\dfrac{1-b/100}{1-g/100} > \dfrac{55}{45} = \dfrac{11}{9} \approx 1.222$, where $b$ and $g$ are the secondary drop-out rates for boys and girls that year.
1996-97: retained fractions are $1-0.673=0.327$ for boys and $1-0.737=0.263$ for girls, so the ratio is $0.327/0.263 \approx 1.243$, which clears $1.222$, so boys are more numerous this year.
1997-98: retained fractions are $0.334$ and $0.270$, giving a ratio of $0.334/0.270 \approx 1.237$, again just above $1.222$, so boys are more numerous here too.
1998-99 and 2000-01: the ratios come out to about $1.176$ and $1.179$ respectively, both below the $1.222$ benchmark, so girls stay more numerous in each of these years.
This ratio test confirms the same pattern found the other way: both 1996-97 and 1997-98 clear the benchmark, so strictly speaking the underlying data supports two of the five listed years, not one, which is why this question is treated here as having ambiguous data.
Let's summarize:
Boys outnumber girls at secondary level exactly when the ratio of their retained fractions exceeds $11/9$.
Both 1996-97 and 1997-98 clear this bar, while 1998-99 onward they do not.
Since the question asks for the year "as compared to the year before it," and 1996-97 has no earlier year in the table to compare with, the year that fits both the numeric test and the comparison requirement is 1997-98.
