The monthly production of electric bulbs by a company during the second half of the year 2021 is shown by the following bar graph. Study the bar graph carefully and answer the question given below. What is the percentage decrement in the production of electric bulbs in October as compared to the production in July? (Correct up to two decimal places.)

Correct — C. The bar graph carries a printed label on every bar, so nothing has to be estimated: July = 550 bulbs and October = 375 bulbs.

Percentage decrement is always measured against the earlier figure, July:
fall = 550 − 375 = 175
175 ⁄ 550 = 7 ⁄ 22 = 0.318181…
× 100 = 31.82% → option (c)

Why the others are wrong

• (a)
  30.28% — 30.28% of 550 is about 166.5, so it needs a fall of roughly 166. The labelled bars give 550 and 375, and that fall is exactly 175.
• (b)
  29.82% — 29.82% answers to a fall of about 164, which survives only if October is read as roughly 386. The bar is labelled 375.
• (d)
  32.28% — 32.28% needs a fall of about 177.5 against July's 550. The four options span only two and a half percentage points, so 175 ⁄ 550 has to be carried to four decimals before rounding.

Percentage change has one rule and one place people lose it: the denominator is the original quantity, the one you are comparing away from.

"October as compared to July" makes July the base. Percentage decrease = (fall ⁄ original) × 100 = (550 − 375) ⁄ 550 × 100.

Reversing the base is not a small error. The same 175 over 375 gives 46.67%, a number that is not on the option list at all — which is a useful signal that the base was wrong.

Key facts

• Percentage decrease = (fall ⁄ original) × 100, with the original as denominator.
• July production is 550 and October production is 375, a fall of 175 bulbs.
• 175 ⁄ 550 simplifies to 7 ⁄ 22 = 31.818…%, which rounds to 31.82%.

Common traps

• Dividing 175 by October's 375 instead of July's 550, which returns 46.67%.
• Truncating 31.818… to 31.81 instead of rounding it to 31.82.

No directly related past PYQ was found.