Question

The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in 2009, by what percent did the number of male students increase in 2009?

Line graph plotting the ratio of male to female students from 2008 to 2012
Ratio of male to female students (2008-2012)
Official answer and solution
Official answer
140
From
Official GATE 2014 answer key

Solution

Extract ratio values from the line graph for 2008 and 2009 to calculate the percentage increase in male students.

  1. Read Values from the Graph:

    • In 2008, the ratio of male to female students is:
      R2008=M2008F2008=2.5  ⟹  M2008=2.5F2008.R_{2008} = \frac{M_{2008}}{F_{2008}} = 2.5 \implies M_{2008} = 2.5 F_{2008}.
    • In 2009, the ratio of male to female students is:
      R2009=M2009F2009=3.0.R_{2009} = \frac{M_{2009}}{F_{2009}} = 3.0.
  2. Apply Given Condition:
    The number of female students doubled in 2009:

    F2009=2×F2008.F_{2009} = 2 \times F_{2008}.
  3. Calculate Male Students in 2009:

    M2009=3.0×F2009=3.0×(2F2008)=6.0F2008.M_{2009} = 3.0 \times F_{2009} = 3.0 \times (2 F_{2008}) = 6.0 F_{2008}.
  4. Percentage Increase in Male Students:

    Percentage Increase=M2009−M2008M2008×100\text{Percentage Increase} = \frac{M_{2009} - M_{2008}}{M_{2008}} \times 100
    =6.0F2008−2.5F20082.5F2008×100= \frac{6.0 F_{2008} - 2.5 F_{2008}}{2.5 F_{2008}} \times 100
    =3.52.5×100=1.4×100=140%.= \frac{3.5}{2.5} \times 100 = 1.4 \times 100 = 140\%.

Hence, the number of male students increased by 140%140\%.

Final answer

140

Common trap

Ignoring the doubling of female students and calculating (3.0 - 2.5)/2.5 = 20%.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2014 Computer Science and Information Technology (CS) Session 2
Question
9 of 65, printed as GA Q.9
Section
General Aptitude

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.