Assistant Provident Fund Commissioner and Enforcement Officer / Accounts Officer (APFC and EO/AO) 2025 recruitment test. Transcribed from the Commission's own booklet (series A, PENA-A-PTS); answer worked out by our faculty — UPSC has published no answer key for this sitting. This question is in Part B. Answer last reviewed 25 August 2026.

In a movie hall, there are three categories of seats : Diamond, Gold and Silver. On a week day, the prices per ticket in these categories are ₹ 500, ₹ 300 and ₹ 200, respectively. But on weekends, the prices are raised to ₹ 800, ₹ 500 and ₹ 300, respectively. There are exactly 10 Diamond seats and the number of Silver seats is double the number of Gold seats. If the hall goes house full in all the shows, which of the following is the excess earning made per show on a weekend ?

(a)₹ 20,000
(b)₹ 23,000
(c)₹ 26,000
(d)₹ 30,000

Answer

Why

Correct — B, (b) ₹ 23,000. Work with the EXTRA charged on each class rather than with the two takings, and then use the fact that seats come in whole numbers.

Step 1 — the extra per ticket. Diamond rises from ₹ 500 to ₹ 800, an extra ₹ 300. Gold rises from ₹ 300 to ₹ 500, an extra ₹ 200. Silver rises from ₹ 200 to ₹ 300, an extra ₹ 100.

Step 2 — the seats. Diamond seats are exactly 10. Let the Gold seats be G; then the Silver seats are 2G.

Step 3 — the excess earning of a full house on a weekend. Excess = 10 × 300 + G × 200 + 2G × 100 = 3,000 + 200G + 200G = 3,000 + 400G. Notice that the Gold and Silver classes contribute equally: Gold has half as many seats but twice the increase.

Step 4 — THE STEP THAT DECIDES THE ANSWER. The stem never says how many Gold seats there are, so the expression 3,000 + 400G cannot be evaluated directly. What it can be tested against is the requirement that G be a whole number of seats. Take each option and solve for G: ₹ 20,000 gives 400G = 17,000, so G = 42.5 — impossible. ₹ 23,000 gives 400G = 20,000, so G = 50 — a whole number. ₹ 26,000 gives 400G = 23,000, so G = 57.5 — impossible. ₹ 30,000 gives 400G = 27,000, so G = 67.5 — impossible. Only one of the four figures can be an excess earning at all, and that is ₹ 23,000.

Check it in full. With G = 50 there are 50 Gold and 100 Silver seats, plus 10 Diamond — a 160-seat hall. Weekday full house: 10 × 500 + 50 × 300 + 100 × 200 = 5,000 + 15,000 + 20,000 = ₹ 40,000. Weekend full house: 10 × 800 + 50 × 500 + 100 × 300 = 8,000 + 25,000 + 30,000 = ₹ 63,000. The difference is ₹ 23,000, as required.

Why the others are wrong

(a)₹ 20,000 — This would need 400G = 17,000, that is 42.5 Gold seats, which no hall has. It is also the figure a candidate reaches by rounding, or by forgetting the ₹ 3,000 that the ten Diamond seats contribute: 400G alone equals ₹ 20,000 when G = 50, so anyone who computes the Gold and Silver excess correctly and then omits the Diamond class lands exactly here. Add the ₹ 3,000.
(c)₹ 26,000 — Requires 57.5 Gold seats. Figures of this kind come from mis-assigning the price rises — for instance giving Silver an increase of ₹ 200 and Gold ₹ 100, which reverses the two. The stem's two uses of 'respectively' bind each price to its class in the order Diamond, Gold, Silver, and that order has to be preserved in both lists.
(d)₹ 30,000 — Requires 67.5 Gold seats. It is the largest figure and the one most likely to be chosen by a candidate who has estimated rather than calculated, or who has computed a weekend TAKING for some assumed hall size instead of the EXCESS over the weekday taking. The question asks for the difference between the two full houses, not for either of them.

Concept

Two techniques are being tested. The first is working with differences: when a problem compares two totals built from the same quantities at different rates, computing the total twice and subtracting is slower and more error-prone than multiplying each quantity by the CHANGE in its rate. The second is using integrality as a constraint. Where a problem leaves a quantity unspecified, the answer often still follows because the quantity must be a whole number — of seats, of people, of items — and only one of the offered figures is consistent with that. In this problem the excess must equal 3,000 + 400G, so it must exceed a multiple of 400 by exactly 3,000; among the four options only ₹ 23,000 does.

This item is a good example of an examiner using the option list as part of the question. The stem is genuinely short of one datum, and the phrase 'which of the following is the excess earning' invites the candidate to test the options rather than to derive a unique number from the text. Recognising that shift — from solving to testing — is what makes the difference between finishing the item and abandoning it as defective.

This item is worth studying as an example of the option list functioning as part of the question. The stem genuinely does not fix the number of Gold seats, so the excess cannot be computed outright; what it can be is tested, because seats are whole things and only one of the four figures corresponds to a whole number of them. Candidates trained to distrust option-testing as a shortcut should note that here it is not a shortcut but the method. Whenever a datum appears to be missing, check whether an integrality requirement, together with the options, supplies it.

Key facts

Price increases on the weekend: Diamond ₹ 300, Gold ₹ 200, Silver ₹ 100 per ticket.
Seats: Diamond 10, Gold G, Silver 2G.
Excess earning per full-house show = 3,000 + 200G + 200G = 3,000 + 400G.
Gold and Silver contribute equally, since Silver has twice the seats and half the increase.
Only ₹ 23,000 makes G a whole number, giving G = 50, Silver 100, and 160 seats in all.
Weekday full house at that size is ₹ 40,000 and the weekend full house ₹ 63,000, a difference of ₹ 23,000.
Computing each class's contribution from the CHANGE in price is faster than computing two totals and subtracting.
Where a problem leaves a count unspecified, the requirement that it be a whole number is often the deciding constraint.

Study next

Problems solved by working with differences rather than totalsInteger constraints in word problems, and how to use the options as a testRatio-based allocation of quantities, such as one class being double anotherPercentage increase applied to several categories at onceRevenue, cost and profit problems with tiered pricing

Common traps

Omitting the fixed Diamond contribution of ₹ 3,000, which lands on a wrong option exactly.
Reversing the Gold and Silver price increases; 'respectively' binds them in order.
Computing a weekend taking instead of the excess over the weekday taking.
Giving up because the number of Gold seats is not stated, instead of testing the options for whole-number consistency.

Revenue and pricing problems are standard in the quantitative block, and this shape — several categories, a change in each rate, and one quantity left free — recurs. When a datum seems to be missing, check whether the answer options are being used to supply it; that is a legitimate and intended part of the method.

Related PYQs

EPFO_EOAO_2017_Q107

The price of an article is increased by 20%. Further, there is a tax of 5% on the increment. If the article costs ₹ 1,331 to the customer, then what was the price of the article before the increase in price?

(a) ₹ 1,000
(b) ₹ 1,064
(c) ₹ 1,100
(d) ₹ 1,200

Answer(c) ₹ 1,100

A pricing problem from the earlier paper worked the same way — a percentage increase and a tax on the increment, where the answer comes from tracking the change rather than recomputing the whole amount.

Practice

practice — not a real PYQ
A hall has 20 seats of class P and three times as many of class Q. On a holiday the price of a P ticket rises by ₹ 100 and that of a Q ticket by ₹ 50. If the hall is full, what is the excess earning on a holiday show ?
- (a)₹ 3,000
- (b)₹ 4,000
- (c)₹ 5,000
- (d)₹ 6,000
Answer(c) ₹ 5,000

Why