Question

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.

Suppose that every year, 7,000 students enter Class I, of which 45% are boys. What was the average number, as a whole number, of girls who stayed on in the education system beyond elementary classes, over the years 1996-97 to 2004-05?

• A. 1475
• B. 1573
• C. 1743
• D. 1673

Hint:

Girls entering each year are 55% of 7,000, that is 3,850; multiply this by (1 minus that year's elementary drop-out rate for girls) for each of the nine years, then average the nine results.

Answer 1

The Correct Option is D

Step 1: Work out how many girls enter Class I each year.
The question says 7,000 students enter Class I every year and boys are 45% of them, so girls are the remaining 55%. That gives \(7000 \times 0.55 = 3850\) girls entering in each of the nine years.

Step 2: Understand what "stayed on beyond elementary classes" means.
A girl who stays on beyond elementary classes is one who does not drop out by the elementary level, Classes I-VIII. If the elementary drop-out rate for girls in a year is \(g\) percent, the fraction who stay on is \((1-g/100)\), so the number of girls who stay on that year is \(3850 \times (1-g/100)\).

Step 3: Apply this to each of the nine years using the elementary girls' drop-out rates from the table.
1996-97 (\(g=59.5\)): \(3850 \times 0.405 = 1559\).
1997-98 (\(g=59.3\)): \(3850 \times 0.407 = 1567\).
1998-99 (\(g=59.2\)): \(3850 \times 0.408 = 1571\).
1999-2000 (\(g=58.0\)): \(3850 \times 0.420 = 1617\).
2000-01 (\(g=57.7\)): \(3850 \times 0.423 = 1629\).
2001-02 (\(g=56.9\)): \(3850 \times 0.431 = 1659\).
2002-03 (\(g=53.5\)): \(3850 \times 0.465 = 1790\).
2003-04 (\(g=52.9\)): \(3850 \times 0.471 = 1813\).
2004-05 (\(g=51.2\)): \(3850 \times 0.488 = 1879\).

Step 4: Add these nine values and divide by 9 for the average.
Adding them up gives \[ 1559+1567+1571+1617+1629+1659+1790+1813+1879 = 15084 \] so the average is \(15084 \div 9 = 1676\), which is close to a whole number of about 1676.
Among the options, 1673 is the nearest whole number to this average, well ahead of 1475, 1573, and 1743, which are all too far from 1676 to be the intended match.

Final Answer:
The average number of girls who stayed on beyond elementary classes, from 1996-97 to 2004-05, is closest to 1673. \[ \boxed{1673} \]