The following bar graph shows the number of students who passed the exam of GATE in the given years. Number of Students 2018 — 140 2019 — 180 2020 — 130 What was the percentage increase in the number of students in 2019 over 2018 (rounded off to two decimal places)?

Correct — C. The stem is an image: a bar graph of students who passed GATE, then the question about the increase from 2018 to 2019.

Read the two bars: 2018 = 140 students, 2019 = 180 students.

Increase = 180 − 140 = 40

Percentage increase is taken on the earlier year:
(40 ⁄ 140) × 100 = 28.5714…

To two decimal places, 28.57% → option (c).

Why the others are wrong

• (a)
  29.52% — 29.52% needs a base of about 135, which sits between the 2018 bar (140) and the 2020 bar (130) and matches neither.
• (b)
  35.79% — 35.79% needs a base near 112, a value no bar in the graph shows. Dividing 40 by 180 gives 22.22% and by 130 gives 30.77%.
• (d)
  32.25% — 32.25% needs a base of about 124. The nearest bar to that is 2020's 130, and even that would give 30.77%, not 32.25%.

Percentage increase always divides by the starting value, never by the finishing one.

% increase = (new − old) ⁄ old × 100. Here old = 140 for 2018 and new = 180 for 2019, so the fraction is 40⁄140, which cancels to 2⁄7.

2⁄7 = 0.285714…, a repeating decimal. That is why the question asks for two decimal places instead of a round figure, and why 28.57% looks unfriendly but is exact to that precision.

Key facts

• Percentage increase = (new − old) ⁄ old × 100.
• The graph reads 140 for 2018, 180 for 2019 and 130 for 2020.
• 40⁄140 = 2⁄7 = 28.5714…, so 28.57% to two decimal places.

Common traps

• Dividing by the 2019 figure of 180 and answering 22.22%
• Bringing the 2020 bar into a question that names only 2018 and 2019

No directly related past PYQ was found.