EPFO APFC 2023 General Studies · Question 105 of 120

Correct — B, (b) Y. This item prints nothing but its own sentence. The Directions block and the earnings-and-profits table it depends on were printed once, above the first question of this set, and they govern this item too; without them the sentence cannot be answered at all, so the table must be carried forward rather than looked for on this page. The word that decides the question is 'relative'. A relative jump is a proportional one — the increase measured against the profit the company started from — as opposed to the absolute jump, which is the increase in units and which the next item of the set asks about. 'Over the previous year' fixes the comparison as 2020 against 2019, not against 2016 and not against the best year in the run. So four small divisions settle it. Company X made a profit of 20·7 in 2019 and 25·8 in 2020, a rise of 5·1 on a base of 20·7, which is about 24·6 per cent. Company Y made 5·5 and then 9·5, a rise of 4 on a base of 5·5, which is about 72·7 per cent. Company Z made 12 and then 14, a rise of 2 on a base of 12, which is 16·7 per cent. Company W made 12·5 and then 20·5, a rise of 8 on a base of 12·5, which is 64 per cent. The largest of the four proportions belongs to company Y, and that is option (b). The comparison that actually needs care is Y against W, since the other two are far behind, and it can be settled in whole numbers without any division. Company Y's profit multiplied by 9·5/5·5, which is 19/11; company W's multiplied by 20·5/12·5, which is 41/25. Cross-multiplying, 19 × 25 = 475 against 41 × 11 = 451, and 475 is the larger, so Y grew proportionally faster than W. Notice what makes this happen: Y's rise of 4 units is the second smallest in the column, half of W's rise of 8, but Y started from 5·5, the smallest profit any company recorded in 2019. A small base magnifies a proportional change, and that single effect is what the question is testing. There is a second reading of the table worth carrying away. Y's profit over the five years runs 8·5, 9·5, 7·5, 5·5, 9·5 — it fell for three years and then returned in 2020 to exactly the figure it had reached in 2017. The largest relative jump in the table is therefore a recovery rather than growth, which is precisely the kind of thing a percentage alone will not tell you.

• (a)X — Company X is the largest and steadiest earner in the table and it recorded the highest profit of any company in 2020, 25·8, so it is the natural choice for a candidate who reads the question as asking which company did best rather than which improved fastest. Its absolute jump of 5·1 is the second largest in that year as well. But size is not the question. Measured against its own 2019 profit of 20·7, the rise of 5·1 is about 24·6 per cent — comfortably the third largest proportional jump of the four, ahead of only company Z. The arithmetic of a large base works against X throughout the table: it would have had to add 4·14 to grow by a fifth and about 10·35 to grow by half, while company Y needed only 1·1 to grow by a fifth. Any question containing the word 'relative', 'proportional' or 'percentage' has to be answered against each company's own starting figure, never against the column's largest number.
• (c)Z — Company Z has the smallest relative jump of the four, not the largest. Its profit went from 12 in 2019 to 14 in 2020, a rise of 2 on a base of 12, which is 16·7 per cent — below X's 24·6 per cent, W's 64 per cent and Y's 72·7 per cent. There are two ways to arrive here. One is to answer the neighbouring question by mistake: the third item of this set asks for a minimum rather than a maximum, and a candidate working quickly through a shared-context set can carry the wrong instruction from one item to the next. The other is to be drawn by the tidiness of the numbers — 12 to 14 is the only pair in the row with no decimal at all, and a clean pair invites a candidate to compute it first and then stop. Z is in fact the most consistent profit-grower in the table, rising every single year from 7·5 to 14, but consistency is not what this item measures.
• (d)W — This is the trap the item is built around, and it is worth understanding rather than merely avoiding. Company W's profit rose from 12·5 in 2019 to 20·5 in 2020, an increase of 8 units, which is the largest absolute jump anywhere in the profit rows for that year — larger than X's 5·1, larger than Y's 4 and four times Z's 2. A candidate who compares the four increases as numbers, without dividing each by the profit it started from, will choose W and will have answered a genuine question about the table; it is simply not the question printed. In relative terms W grew by 8/12·5, which is 64 per cent, against Y's 4/5·5, which is about 72·7 per cent. The whole-number check confirms it: 19 × 25 = 475 against 41 × 11 = 451. W is also the company the next item of this set is not about, and keeping the two questions apart — relative here, absolute there — is the discipline the set exists to test.

Absolute change and relative change are different measurements of the same movement, and a table like this one is designed so that they point at different rows. The absolute change is simply the later value minus the earlier one, expressed in the units of the table. The relative change is that difference divided by the earlier value, usually expressed as a percentage. Because the divisor differs from row to row, the ordering by absolute change and the ordering by relative change need not agree, and in this table they do not: the largest absolute rise in 2020 belongs to company W and the largest relative rise to company Y. The mechanism is the base effect. A quantity starting from a small figure can post a very large percentage rise on a modest absolute movement, while a quantity starting from a large figure needs a correspondingly large movement to show the same percentage. This is why growth rates for small economies, small companies and small programme budgets look dramatic, and why a careful reader always asks what the base was before being impressed by a percentage. Two practical techniques follow. First, compare ratios rather than percentages: the ordering of new/old is the same as the ordering of the percentage rises, and ratios can be compared by cross-multiplication in whole numbers. Second, when a question offers four entities and two are obviously out of contention, do the exact comparison only for the remaining pair; here that reduces four divisions to one cross-multiplication.

This is the middle item of the three-question set governed by the table printed above the first of them, and it is the only place in this booklet outside the English Language section where a question cannot be answered from the words printed under its own number. That has a practical consequence: a candidate who has turned the page, or who attempts questions out of order, will find a one-line sentence naming four letters and no data whatsoever. The set has to be attempted as a set. The design of the three items is the more interesting thing. The first asks a threshold count on earnings, this one asks for a maximum relative change in profit, and the third asks for a minimum absolute change in profit — so across three questions the examiner switches the row, the direction of the comparison and the kind of change being measured. Nothing can be carried from one to the next except an understanding of the table itself, which is exactly what a shared-context set is for. The vocabulary is the lever here. 'Relative' and 'absolute' are used precisely and in adjacent questions, and a candidate who treats them as interchangeable will get one of the two wrong whichever way the guess falls. Reading the single adjective carefully is worth more marks in this set than any arithmetic in it, and the arithmetic itself — four small divisions, or one cross-multiplication — is well under a minute's work.

• Relative change is the increase divided by the value it started from; absolute change is the increase itself. In the 2020 profit column the two measures disagree: company W posted the largest absolute jump, 8 units from 12·5 to 20·5, while company Y posted the largest relative jump, 4 units on a base of 5·5, which is about 72·7 per cent against W's 64 per cent.
• The four relative jumps in 2020 over 2019 are: X, 5·1 on 20·7, about 24·6 per cent; Y, 4 on 5·5, about 72·7 per cent; Z, 2 on 12, about 16·7 per cent; W, 8 on 12·5, 64 per cent. Only Y and W are in contention, and the rest of the arithmetic can be skipped once that is seen.
• Two growth rates can be compared without dividing at all. Y's profit multiplied by 19/11 and W's by 41/25; cross-multiplying gives 19 × 25 = 475 against 41 × 11 = 451, so Y grew faster. Comparing new/old ratios by cross-multiplication avoids decimals entirely and is the safest method on close cases.
• The base effect is the reason the answer is Y: it began 2019 with the smallest profit in the table, 5·5, so a modest four-unit recovery became the largest proportional gain. A small base magnifies percentage change, which is why any percentage should be read together with the figure it was calculated on.
• Y's profit across the five years runs 8·5, 9·5, 7·5, 5·5, 9·5 — three years of decline followed by a return in 2020 to exactly its 2017 level. The table's largest relative jump is therefore a recovery to a previous figure rather than genuine growth, a distinction a percentage on its own conceals.

• Answering with the largest absolute jump. Company W's profit rose by 8 units, the largest single increase in the 2020 column, but on a base of 12·5 that is 64 per cent, less than company Y's 72·7 per cent on a base of 5·5. The adjective 'relative' is the whole question.
• Choosing the biggest company. Company X recorded the highest profit in 2020 at 25·8 and the second largest increase, but measured against its own large base its growth is only about 24·6 per cent, third of the four. Size and growth rate are independent readings of a table.
• Carrying the previous item's instruction across. The three questions in this set switch between earnings and profits, between maximum and minimum and between relative and absolute; the third asks for a minimum absolute jump, and answering that question here gives company Z.
• Comparing against the wrong year. 'Over the previous year' means 2019, so the 2019 profits are the bases. Using 2016 as the base instead would compare Y's 9·5 with 8·5 and reduce the largest relative jump in the table to a rise of about twelve per cent.

Within a shared-context data set, the maximum-or-minimum item is the standard second question, and it is where the examiner plants the absolute-versus-relative distinction. The pattern to expect is a pair of adjacent items that use the same rows but opposite measures, exactly as this set does — a relative maximum here and an absolute minimum in the next question — so that a candidate who is careless about one adjective loses both marks rather than one. Other regular forms in this position ask which entity showed the largest change in a derived quantity such as a margin or a share of the total, which entity was above or below the column average, and in which year a given entity performed best. All of them reward the same preparation: read the adjective, identify the two candidates that could plausibly win, and settle the pair exactly rather than computing all four values. Since the table is shared, the orientation cost is paid once, so the arithmetic per item should be kept to a minimum and the reading done with care.

No directly related past PYQ was found.

• practice — not a real PYQ

  Four departments of a firm recorded these profits in two successive years: P rose from 8 to 11, Q from 25 to 33, R from 40 to 51 and S from 15 to 20. Which department's profit showed the largest percentage increase?

  • (a)P
  • (b)Q
  • (c)R
  • (d)S

  Answer(a) P — the increases are P 3 on 8, that is 37·5 per cent; Q 8 on 25, that is 32 per cent; R 11 on 40, that is 27·5 per cent; S 5 on 15, that is 33·3 per cent. P wins on the smallest base even though its rise of 3 is the smallest of the four in absolute terms, while R, whose rise of 11 is the largest in absolute terms, comes last. That inversion is the whole point of the item.

• practice — not a real PYQ

  In one year, company A's profit rose from ₹12 crore to ₹15 crore and company B's profit rose from ₹20 crore to ₹23 crore. Which one of the following statements is correct?

  • (a)A's percentage increase in profit is greater than B's
  • (b)B's percentage increase in profit is greater than A's
  • (c)The percentage increases are equal because the absolute increases are equal
  • (d)The percentage increases cannot be compared without knowing the earnings

  Answer(a) A's percentage increase in profit is greater than B's — both profits rose by exactly ₹3 crore, but A's rise is 3 on a base of 12, which is 25 per cent, while B's is 3 on a base of 20, which is 15 per cent. Equal absolute change on a smaller base always gives the larger percentage, and the earnings figures are not needed at all, since a percentage change in profit is computed on the earlier profit.