In all the five years, the number of students getting employment in Hardware…

Concept

A percentage in a share table is not a head count. Every year in this table carries its own base — the number of students who passed out that year — so the same percentage stands for a different number of students in different years.

Students placed in an area in a given year = (that area's share for the year ÷ 100) × that year's total pass-outs. Because the bases differ from year to year, shares belonging to different years must never be added or subtracted as percentages; convert every share into a count first, aggregate the counts, and compare only then.

Application

1. Note the base for each year: 800 in 2019, 600 in 2020, 1,100 in 2021, 1,200 in 2022 and 1,000 in 2023.

2. Turn the Hardware shares 22%, 17%, 23%, 19% and 32% into counts: 176, 102, 253, 228 and 320.

3. Turn the SQA shares 36%, 48%, 43%, 37% and 32% into counts: 288, 288, 473, 444 and 320.

4. Aggregate each area across the five years: Hardware gives 176 + 102 + 253 + 228 + 320 = 1,079 and SQA gives 288 + 288 + 473 + 444 + 320 = 1,813.

5. Take the difference between the two five-year totals: 1,813 − 1,079 = 734.

Cross-check

Adding the year-by-year gaps independently reproduces the same figure: 112 + 186 + 220 + 216 + 0 = 734, so the two five-year totals were aggregated correctly.

The year 2023 adds nothing to the gap because Hardware and SQA both stand at 32% of the very same 1,000 pass-outs. This also shows why the raw share differences must not simply be added: 14 + 31 + 20 + 18 + 0 = 83 percentage points sits on five different bases and measures nothing.

Across 2019–2023 the number of students placed in Hardware falls short of the number placed in SQA by 734.