Enforcement Officer / Accounts Officer (EO/AO) 2020 recruitment test, advertisement 421. Transcribed from the Commission's own booklet (series A, NMJX-U-GTA); answer as per the official UPSC final answer key. This question is in Part B. Answer last reviewed 24 August 2026.

40% of the students in a class are from India and 50% are girls. If 25% of the Indian students are girls, what percentage of non-Indian students are boys ?

(a)33·33%
(b)40%
(c)25%
(d)20%

Answer

Why

Correct — A, (a) 33·33% — the booklet prints the decimal point as a raised middle dot. The step that decides this question is the base. Every percentage in the stem is taken on a different group, and the one the question asks for is taken on the non-Indian students, not on the class. Take the class as 100 students, which is always the right first move when only percentages are given. Indian students: 40. Girls in the class: 50. Indian students who are girls: 25% of 40 = 10. From those three numbers the whole table fills in. Non-Indian students are 100 - 40 = 60. Girls who are not Indian are 50 - 10 = 40. Boys who are not Indian are therefore 60 - 40 = 20. The question asks what percentage of non-Indian students are boys, so the 20 is measured against the 60 non-Indian students: 20/60 = 1/3 = 33·33%. Laying it out as a two-by-two table makes the structure visible and takes about fifteen seconds: with Indian and non-Indian as the columns and girls and boys as the rows, the entries are 10 and 40 across the girls' row, 30 and 20 across the boys' row, columns totalling 40 and 60 and rows totalling 50 and 50, everything adding to 100. Every question that can be asked about this class is then read straight off the table. Note the trap the option list is built around: 20 is the number of non-Indian boys, and as a share of the whole class that is 20%, which is printed as the fourth option. The same count gives two different percentages depending on what it is divided by, and the question names its base explicitly — 'of non-Indian students'. Note also that these four options are not printed in ascending order: they run 33·33%, 40%, 25%, 20%, which is the Commission's own arrangement.

Why the others are wrong

(b)40% — 40% is a number that genuinely appears twice in this class, and neither appearance answers the question. Forty per cent of the students are Indian, which is given in the first line of the stem; and 40 of the 100 students are non-Indian girls, which is what the table produces for that cell. A candidate who computes the non-Indian girls correctly and then reports that count as though it were the answer arrives here, having done the harder half of the work and stopped one step early — the question asks about boys, and about their share of the non-Indian group rather than of the class. As a share of the non-Indian students, the girls are 40 out of 60, which is 66·67%, and the boys make up the remaining 33·33%. Those two must add to a hundred, which is a quick way to check any answer of this shape.
(c)25% — 25% is lifted straight from the stem, where it is the proportion of the Indian students who are girls, and options built from a number the question has already supplied are the commonest kind in percentage items. It answers a different question about a different group: of the 40 Indian students, 10 are girls and 30 are boys, so 25% of the Indians are girls and 75% of them are boys. Neither figure describes the non-Indian students, who are the group the stem asks about. The defence is mechanical and worth making a habit — underline the group named in the question before starting, because a percentage without its base is not a quantity at all, and every number in a problem like this is a percentage of something different.
(d)20% — 20% is the right count with the wrong base, and it is the option this item is really built to catch. There are indeed 20 non-Indian boys, and out of a class of 100 students that is 20% — a true statement about the class. But the question asks what percentage of non-Indian students are boys, and there are only 60 non-Indian students, so the same 20 becomes 20/60, which is 33·33%. A candidate who fills the table correctly and then divides by the wrong total loses the mark at the last step, which is why it is worth writing the base down explicitly as a fraction — 20 out of 60 — before converting to a percentage. The general rule is that a percentage of a subgroup must be measured against that subgroup, and a number that has just been derived as a share of the whole is not it.

Concept

A percentage is a fraction with a stated base, and the entire difficulty of this family of questions lies in keeping track of which base each figure belongs to. When a population is divided in two independent ways at once — here by nationality and by sex — the right tool is a two-by-two table, sometimes called a contingency table. Draw the two categories as columns and the other two as rows, add a total row and a total column, and the grid has nine cells of which only three or four are usually given; the rest follow, because every row and every column must add up. Set the total to 100 whenever the stem gives only percentages, since that makes every entry a count and a percentage of the whole at the same time and removes fractions from the working entirely. The second idea is conditional proportion. 'Twenty-five per cent of the Indian students are girls' is not a statement about the class; it is a statement about a subgroup, and it converts into a count only after being multiplied by the size of that subgroup. The same count then yields different percentages depending on what it is divided by, which is exactly what separates the keyed option from the last one here. Reading the phrase that names the base — 'of the Indian students', 'of non-Indian students' — is therefore the whole skill.

Percentage questions are the most common single form in EPFO EO/AO quantitative blocks, because they need no formula and can be made hard purely by nesting one proportion inside another. This item is a clean example: the arithmetic never leaves whole numbers until the final division, and yet three of the four options correspond to real quantities in the same class. That design is worth understanding, because it tells a candidate where to be careful. The risk is not miscalculation; it is answering a neighbouring question. The discipline that follows is to write the table, and then to re-read the actual ask before choosing a cell. Fifteen seconds of grid and five seconds of re-reading beats any shortcut. There is also a presentational point on this item. The four options are printed out of numerical order — 33·33%, 40%, 25%, 20% — so a candidate scanning for the largest or smallest value cannot rely on position, and the decimal point in the first option is set as a raised middle dot in this booklet's house style rather than as a full stop.

Key facts

A percentage means nothing without its base. The same count of 20 non-Indian boys is 20% of the class of 100 and 33·33% of the 60 non-Indian students, and the question names which base it wants.
Taking the population as 100 whenever a stem gives only percentages turns every figure into a whole-number count and removes fractions from the working, which is the single most useful habit in this topic.
The completed table for this class: Indian girls 10, non-Indian girls 40, Indian boys 30, non-Indian boys 20, with columns of 40 and 60, rows of 50 and 50, and a grand total of 100.
The working for the answer: 25% of the 40 Indian students gives 10 Indian girls; 50 - 10 = 40 non-Indian girls; 60 - 40 = 20 non-Indian boys; and 20 out of 60 is one-third, or 33·33%.
A cross-check that costs nothing: within any subgroup the boys' and girls' percentages must add to a hundred, and 33·33% with 66·67% does, while 20% with any of the other options does not.
The four options on this item are printed out of numerical order — 33·33%, 40%, 25%, 20% — and the decimal point in the first is set as a raised middle dot, both being the Commission's own typography.

Every percentage has a base — and the stem names the one it wants

Take the class as 100 students→Always the right first move when a stem gives only percentages: every figure becomes a whole-number count and a percentage of the whole at the same time, and fractions disappear from the working.

The three numbers the stem gives→Indian students, 40. Girls in the class, 50. Indian students who are girls, 25% of 40 = 10.

The rest of the table fills itself in→Non-Indian students = 100 − 40 = 60. Non-Indian girls = 50 − 10 = 40. Non-Indian boys = 60 − 40 = 20. Laid out with Indian and non-Indian as the columns and girls and boys as the rows: 10 and 40 across the girls’ row, 30 and 20 across the boys’ row, columns totalling 40 and 60, rows totalling 50 and 50, and everything adding to 100. Every question that can be asked about this class is then read straight off the grid.

20 ÷ 60 = 1/3 = 33·33%→The question asks what percentage of NON-INDIAN STUDENTS are boys, so the 20 is measured against the 60 non-Indian students and not against the class.

The trap the option list is built around→20 is the number of non-Indian boys, and as a share of the whole class of 100 that is 20% — printed as the fourth option, and a true statement about the class. The same count gives two different percentages depending on what it is divided by. A cross-check that costs nothing: within any subgroup the boys’ and girls’ percentages must add to a hundred, and 33·33% with 66·67% does, while 20% with any of the other options does not.

Where 40% and 25% come from→40 appears twice in this class and neither appearance answers the question: forty per cent of the students are Indian, given in the stem’s first line, and 40 of the 100 are non-Indian girls, which is the count a candidate reports as though it were the percentage asked for. 25% is lifted straight from the stem, where it is the proportion of the INDIAN students who are girls — of the 40 Indians, 10 are girls and 30 are boys. Note also that the four options are printed out of numerical order, 33·33%, 40%, 25%, 20%, and that the decimal point is set as a raised middle dot.

Study next

Two-way classification problems set with a contingency table, including those that ask for a count rather than a percentageSuccessive percentage changes, where a quantity is increased and then decreased and the base shifts between the two stepsPercentage increase and decrease, and the difference between a change of x percentage points and a change of x per centProfit, loss and discount, which are percentage questions with a fixed vocabulary for the base — cost price, selling price and marked priceSimple problems on averages and ratios stated as percentages of a whole, which appear alongside these in every quantitative block

Common traps

Dividing by the wrong total at the last step. The count of non-Indian boys is 20, but the question asks for their share of the 60 non-Indian students, not of the class of 100, and both answers are printed as options.
Choosing a number that appears in the stem. Here 25% is the proportion of Indian students who are girls, a figure the question supplies rather than asks for, and options of that kind are standard in percentage items.
Stopping one step early. Computing the 40 non-Indian girls is most of the work, but the ask is about boys and about a share, so the count has to be turned into a proportion of the right group.
Assuming the option list is ordered. These four run 33·33%, 40%, 25%, 20%, which is neither ascending nor descending, so no reasoning about position in the list is available.

Percentages are the backbone of the EPFO EO/AO quantitative blocks and appear in two shapes. The first is a straight computation of a percentage change or a successive change. The second, of which this item is a textbook instance, is a population split two ways at once, where the mark depends on identifying the base rather than on any arithmetic. Stems in this second family are one or two sentences and always contain a phrase naming the group — 'of the Indian students', 'of non-Indian students' — which is the examiner telling the candidate where the difficulty is. Options are built from other true quantities in the same population, so an answer that feels familiar is no evidence at all. The same structure reappears in the accountancy and labour-law blocks whenever a rate is applied to one class of employee and a share of another is asked for.

Related PYQs

EPFO_EOAO_2020_Q24Open & attempt →

Suppose x and y are two positive numbers such that when x is reduced by 2 and y is increased by 2, the ratio becomes 2 : 1; and when x is increased by 2 and y is reduced by 2, the ratio becomes 3 : 1. Which one of the following is equal to x – y ?

(a) 20
(b) 24
(c) 18
(d) 22

Answer(a) 20

The ratio item from the earlier quantitative block, where two quantities are altered and a new ratio is given. Both are about keeping track of what each number is measured against, and both punish a step taken before the ask has been read.

EPFO_EOAO_2020_Q119Open & attempt →

The average weight of 100 students in a class is 46 kg. The average weights of boys and girls are 50 kg and 40 kg respectively. What is the difference between the number of boys and girls ?

(a) 30
(b) 25
(c) 20
(d) 10

Answer(c) 20

The class-average item one question later, where a group is again split into boys and girls and the split has to be recovered. Read together they show the two ways a paper divides a population: by proportion, and by a weighted mean.

Practice

practice — not a real PYQ
In a class, 60% of the students are boys and 25% of the boys wear spectacles. What percentage of the whole class is made up of boys who wear spectacles ?
- (a)10%
- (b)15%
- (c)20%
- (d)25%
Answer(b) 15%
practice — not a real PYQ
In an office, 60% of the employees are men and 50% of all the employees are graduates. If 20% of all the employees are men who are graduates, what percentage of the women employees are graduates ?
- (a)30%
- (b)50%
- (c)75%
- (d)80%
Answer(c) 75%

Why