What is the ratio of percentage decline in votes of B in May in comparison to…

Concept — a percentage decline always measures a fall against the earlier (base) value: percentage decline = (initial value − final value) ÷ initial value × 100. Because the base is the starting figure, two quantities that fall by the very same absolute amount still show different percentage declines whenever they start from different values — the smaller starting value produces the larger percentage decline.

Application — pick the two rows the question names and apply that formula to each separately.

1. B polled 2.5 lakh votes in January and 1.0 lakh votes in May, so B’s absolute fall is 2.5 − 1.0 = 1.5 lakh.

2. Percentage decline for B = (1.5 ÷ 2.5) × 100 = 60%.

3. C polled 3.0 lakh votes in January and 1.5 lakh votes in November, so C’s absolute fall is 3.0 − 1.5 = 1.5 lakh.

4. Percentage decline for C = (1.5 ÷ 3.0) × 100 = 50%.

5. Required ratio = 60 : 50 = 6 : 5.

Cross-check — both companies shed exactly the same 1.5 lakh votes, so the bigger percentage decline has to belong to the one with the smaller January base. Dividing the two percentages directly gives (1.5 ÷ 2.5) ÷ (1.5 ÷ 3.0) = 3.0 ÷ 2.5, so the ratio of the percentage declines is simply the reverse ratio of the two January figures, 3.0 : 2.5 = 6 : 5. A common slip is to compare the absolute falls instead — both are 1.5 lakh, which would wrongly suggest 1 : 1 — or to divide the fall by the later figure rather than the January figure.