Enforcement Officer / Accounts Officer (EO/AO) 2017 recruitment test. Transcribed from the Commission's own booklet (series A, GRS-A-TNS); answer as per the official UPSC final answer key. This question is in Part B. Answer last reviewed 24 August 2026.

Consider the following information : Rate of gross profit—25% on cost of goods sold Sales—₹ 20,00,000 Which one of the following is the amount of gross profit?

(a)₹ 5,00,000
(b)₹ 6,25,000
(c)₹ 3,75,000
(d)₹ 4,00,000

Answer

Why

Correct — D, (d) ₹ 4,00,000. Everything in this item turns on four words in the data line: the rate of gross profit is 25 per cent on cost of goods sold, not on sales. A percentage is meaningless until you know its base, and here the base given is cost while the figure supplied is sales, so the rate has to be converted before it can be used.

The conversion is easiest done on a scale of 100. If cost is 100, then a gross profit of 25 per cent on cost is 25, and sales are 100 + 25 = 125. Gross profit as a fraction of sales is therefore 25/125, which is 1/5, or 20 per cent. Applying that to the sales figure given: ₹ 20,00,000 × 20% = ₹ 4,00,000.

The answer checks back cleanly, which is the habit worth building on any item of this shape. If gross profit is ₹ 4,00,000, the cost of goods sold is ₹ 20,00,000 − ₹ 4,00,000 = ₹ 16,00,000, and 25 per cent of ₹ 16,00,000 is ₹ 4,00,000. The rate on the stated base is reproduced exactly.

The general rule is worth carrying in both directions, because papers set it both ways. If gross profit is x per cent on cost, it is x/(100 + x) of sales; if it is y per cent on sales, it is y/(100 − y) of cost. A quarter on cost is a fifth on sales; a third on cost is a quarter on sales; a fifth on cost is a sixth on sales. The pattern to remember is that the rate on cost is always the larger of the two figures, because cost is the smaller base — so a conversion that makes the percentage bigger when moving from cost to sales has gone the wrong way.

Why the others are wrong

(a)₹ 5,00,000 — ₹ 5,00,000 is 25 per cent of the sales figure, and it is the answer to the question the item is pretending to ask. It comes from reading past the words 'on cost of goods sold' and applying the given rate to the only number in sight. The check disposes of it in one line: if gross profit were ₹ 5,00,000, cost of goods sold would be ₹ 15,00,000, and ₹ 5,00,000 is 33.33 per cent of ₹ 15,00,000, not the 25 per cent the data specify. This is the single commonest error in gross profit computations, and the reason the base of a percentage should be written down before any arithmetic is attempted.
(b)₹ 6,25,000 — ₹ 6,25,000 is 25 per cent of ₹ 25,00,000, which is the sales figure grossed up by a further 25 per cent. It is the result of applying the mark-up in the wrong direction — multiplying by 1.25 where the situation called for dividing by it. Sales already include the gross profit and are therefore the larger of the two figures; inflating them again produces a cost of goods sold larger than the sales themselves, which cannot be right in a business that is making a profit.
(c)₹ 3,75,000 — ₹ 3,75,000 is 25 per cent of ₹ 15,00,000, where ₹ 15,00,000 is the sales figure reduced by 25 per cent. It comes from treating the given rate first as a margin on sales, to arrive at a cost, and then applying the same rate again to that cost. Two mistakes have been made and they partly cancel, which is what makes the figure look plausible; it lies below the correct answer, whereas the other wrong figures lie above it. Checking back exposes it at once: if gross profit were ₹ 3,75,000, cost of goods sold would be ₹ 16,25,000, and ₹ 3,75,000 is about 23 per cent of that, not 25.

Concept

Gross profit is the excess of net sales over the cost of goods sold, and cost of goods sold is opening stock plus purchases and direct expenses, less closing stock. The gross profit ratio can be expressed on either of two bases and the two are not interchangeable. Expressed on cost it is a mark-up: the amount added to cost to arrive at the selling price. Expressed on sales it is a margin: the share of the selling price that is profit. Because sales exceed cost by the profit itself, the mark-up percentage is always the higher figure, and the two are linked by mark-up = margin ÷ (1 − margin) and margin = mark-up ÷ (1 + mark-up). The relationship matters far beyond a direct question of this kind. It is used to work out a missing figure in a Trading Account, to estimate the value of stock destroyed by fire when preparing a memorandum trading account for an insurance claim, to check whether a physically counted stock is plausible, and to build the gross profit ratio used in ratio analysis of a company's profitability.

This paper's accountancy block prefers items whose difficulty is a definition rather than a calculation, and this one is the purest example: the arithmetic is a single multiplication, and the whole question is whether the candidate noticed the base. The Commission has been careful about it — the phrase 'cost of goods sold' is set on its own line, indented further to the right, so it reads as part of the same datum and cannot be dismissed as a stray. Three of the four options are the figures produced by the three natural ways of getting the base wrong, so a candidate who converts carelessly will find his answer waiting for him on the list. The habit that protects against this is to write the base beside every rate before doing anything with it.

Key facts

Gross profit of 25 per cent on cost equals 20 per cent on sales: 25/125 = 1/5.
Here: ₹ 20,00,000 × 20% = ₹ 4,00,000, with cost of goods sold ₹ 16,00,000 and 25% of that ₹ 4,00,000.
If gross profit is x per cent on cost, it is x/(100 + x) of sales; if y per cent on sales, it is y/(100 − y) of cost.
A quarter on cost is a fifth on sales; a third on cost is a quarter on sales; a fifth on cost is a sixth on sales.
The rate expressed on cost is always the larger of the two, because cost is the smaller base.
Cost of goods sold = opening stock + purchases + direct expenses − closing stock.
The same conversion is used in a memorandum trading account to estimate stock destroyed by fire.

A percentage is meaningless until you know its base

The base given is cost; the figure given is sales→The rate of gross profit is 25 per cent on cost of goods sold, not on sales, so the rate has to be converted before it can be used on the number supplied.

On a scale of 100→If cost is 100, then a gross profit of 25 per cent on cost is 25, and sales are 100 + 25 = 125. Gross profit as a fraction of sales is therefore 25/125, which is 1/5, or 20 per cent.

₹ 20,00,000 × 20% = ₹ 4,00,000→And it checks back cleanly: cost of goods sold is ₹ 20,00,000 − ₹ 4,00,000 = ₹ 16,00,000, and 25 per cent of ₹ 16,00,000 is ₹ 4,00,000. The rate on the stated base is reproduced exactly.

(a) ₹ 5,00,000 — the commonest error→25 per cent of the sales figure, reached by reading past the words 'on cost of goods sold' and applying the given rate to the only number in sight. If gross profit were ₹ 5,00,000, cost of goods sold would be ₹ 15,00,000 — and ₹ 5,00,000 is 33.33 per cent of that, not the 25 per cent the data specify.

(b) ₹ 6,25,000 and (c) ₹ 3,75,000→₹ 6,25,000 is 25 per cent of the sales figure grossed up by a further 25 per cent — the mark-up applied in the wrong direction, which produces a cost of goods sold larger than the sales. ₹ 3,75,000 treats the rate first as a margin on sales and then applies it again to the resulting cost: two mistakes that partly cancel, which is what makes it look plausible.

The rule, in both directions→If gross profit is x per cent on cost it is x/(100 + x) of sales; if y per cent on sales it is y/(100 − y) of cost. A quarter on cost is a fifth on sales, a third on cost a quarter on sales, a fifth on cost a sixth on sales. The rate expressed on cost is always the larger of the two, because cost is the smaller base.

Study next

Memorandum trading account and the estimation of stock lost in a fireTrading Account and the missing-figure problems built on the gross profit ratioGross profit ratio, net profit ratio and operating ratio in ratio analysisStock turnover ratio and its link to the gross profit ratioSingle-entry and incomplete records, where a gross profit percentage is often the only route to the missing figure

Common traps

Applying a rate stated on cost directly to the sales figure. Write the base down before using the rate.
Converting in the wrong direction, so that the rate on sales comes out higher than the rate on cost.
Multiplying sales by one plus the mark-up instead of dividing by it when working back to cost.
Failing to check the answer against the stated base, which catches every one of these errors in a single line.
Reading the second, further-indented line of the data as a separate item rather than as part of the same datum.

Percentage-base items appear in every EPFO accountancy section in one form or another, because they can be set in two lines and cannot be guessed. The direct form asks for the gross profit given a rate on one base and a figure on the other, as here. The applied forms are commoner in longer papers: estimate the stock destroyed by fire, complete a Trading Account with one figure missing, or find sales when cost and mark-up are given. All of them are the same conversion, so it is worth learning the small table of equivalents — a quarter on cost is a fifth on sales, a third on cost is a quarter on sales — rather than deriving it each time under pressure.

Related PYQs

EPFO_EOAO_2017_Q61Open & attempt →

From the information given below, calculate the sum insurable : Date of fire—01.03.2016 Turnover from 01.03.2015 to 29.02.2016—₹ 88,00,000 Agreed GP ratio—20% Special circumstances clause provided for the increase of turnover by 10%

(a) ₹ 19,36,000
(b) ₹ 48,40,000
(c) ₹ 10,32,000
(d) ₹ 24,20,000

Answer(a) ₹ 19,36,000

The insurance item earlier in this block, where the same mark-up-versus-margin confusion supplies the most tempting wrong option — there the ratio is given on turnover and must be left alone.

Practice

practice — not a real PYQ
If gross profit is 20% on sales, gross profit expressed as a percentage of cost of goods sold is
- (a)16.67%
- (b)20%
- (c)25%
- (d)33.33%
Answer(c) 25%
practice — not a real PYQ
Cost of goods sold is ₹ 6,00,000 and gross profit is one-third of the cost of goods sold. Sales are
- (a)₹ 7,50,000
- (b)₹ 8,00,000
- (c)₹ 9,00,000
- (d)₹ 6,00,000
Answer(b) ₹ 8,00,000

Why