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
Why
Correct — C, (c) ₹ 1,100. Everything in this item turns on one phrase — the tax is 5% on the increment, not 5% on the new price. The increment is the rise of 20%, so the tax is five per cent of that rise and not of the whole amount. Get that base right and the problem is a single division.
Let the original price be P. The rise is 0·20 P, so the price after the increase is 1·20 P. The tax is 5% of the rise alone, that is 0·05 × 0·20 P = 0·01 P. What the customer pays is therefore P + 0·20 P + 0·01 P = 1·21 P. Setting that equal to 1,331 gives P = 1,331 ÷ 1·21 = ₹ 1,100, which is option (c).
Read forwards, the check takes seconds and is worth doing. Start at ₹ 1,100. A rise of 20% is ₹ 220, taking the price to ₹ 1,320. Tax at 5% on the increment of ₹ 220 is ₹ 11. The customer pays 1,320 + 11 = ₹ 1,331, exactly the figure in the stem. The arithmetic is also friendlier than it looks, because 1,331 is 11 × 11 × 11 and 1·21 is 1·1 × 1·1, so the division cancels neatly to 1,100.
The option set itself confirms which reading of the tax was intended. Had the 5% been charged on the whole increased price, the multiplier would have been 1·20 × 1·05 = 1·26, and 1,331 ÷ 1·26 is about 1,056 — a figure that appears nowhere among the four choices. When a phrase in a stem admits two readings, working out what each reading would produce and seeing which one lands on an offered value is a legitimate way to settle it.
Why the others are wrong
- (a)₹ 1,000 — A thousand is the figure a candidate reaches by treating 1,331 as a compound-interest total: 1,331 = 1,000 × 1·1 × 1·1 × 1·1, three successive rises of ten per cent. The cube is real and the temptation to use it is strong, because 1,331 is a number that almost announces itself as eleven cubed. But the stem describes one rise of twenty per cent followed by a small tax, not three rises of ten, and a number's arithmetic properties are not evidence about the process that produced it. The forward check settles it: ₹ 1,000 raised by 20% is ₹ 1,200, tax at 5% on the increment of ₹ 200 is ₹ 10, and the customer would pay ₹ 1,210, not ₹ 1,331. A recognisable number in a stem is often a convenience placed there by the examiner to make the division clean, and sometimes a lure; the way to tell is to test it forwards.
- (b)₹ 1,064 — This is the reverse-percentage error, the commonest mistake in the whole topic. A candidate who knows the final amount is above the original by roughly twenty per cent takes twenty per cent off the final amount instead of dividing by 1·21: 1,331 × 0·8 = 1,064·8, which rounds to the figure offered. Reducing by twenty per cent and increasing by twenty per cent are not inverse operations, because the two percentages are taken on different bases — the first on the larger amount, the second on the smaller. The forward check exposes the gap: ₹ 1,064 raised by 20% is ₹ 1,276·80, plus 5% of the increment of ₹ 212·80, which is ₹ 10·64, giving ₹ 1,287·44 and not ₹ 1,331. To undo a rise of x per cent, divide by (1 + x ÷ 100); never subtract.
- (d)₹ 1,200 — Twelve hundred is a round number that sits comfortably below 1,331 and is what a candidate produces by taking roughly ten per cent off the final figure in the head, or simply by reaching for the tidiest option available. It does not survive a forward test. Starting at ₹ 1,200, a rise of 20% is ₹ 240, taking the price to ₹ 1,440; tax at 5% on the increment of ₹ 240 is ₹ 12; the customer would pay ₹ 1,452, which overshoots the stem's figure by ₹ 121. The overshoot is large enough to be visible without a calculator, which is the point worth carrying away: on percentage items the four options are usually far enough apart that a single forward pass through the process will accept one and reject the rest, and that pass is often quicker than solving the equation.
Concept
Percentage change problems are decided by the base — the quantity that the percentage is a percentage of. Every error in the topic can be traced to applying a percentage to the wrong base, and this item is built precisely on that point, because it charges the tax on the increment rather than on the price. Two techniques cover almost all of the ground. The first is the multiplier: an increase of x per cent multiplies a quantity by (1 + x ÷ 100) and a decrease multiplies it by (1 − x ÷ 100), so successive changes are handled by multiplying the factors together, and a change applied to only part of the amount is handled by building the factor from its parts, as 1 + 0·20 + 0·01 was built here. The second is reversal: to recover the original from the final amount, divide by the multiplier rather than subtracting the percentage, because a rise and a fall of the same percentage are taken on different bases and do not cancel — a price raised by 20% and then cut by 20% ends at 96% of where it began. A third habit ties the two together: once a candidate value is in hand, put it forward through the process described in the stem and see whether the stated final amount appears.
Percentages are the most heavily represented single topic in the quantitative half of an EPFO paper, and this item shows why the Commission likes them for an Enforcement Officer's paper in particular. The work of the post involves reading a computation someone else has made — of wages, of contributions, of interest, of damages — and deciding whether the right rate has been applied to the right base. That is exactly this question. The phrase 'tax of 5% on the increment' is doing all the work, and a candidate who reads it as 'tax of 5%' and applies it to the whole price will produce a figure that does not appear among the options and will then waste time hunting for an arithmetic slip that is not there. The lesson is that in a percentage problem the sentence identifying the base deserves more attention than the numbers do.
Key facts
- An increase of x per cent multiplies a quantity by (1 + x ÷ 100); successive changes are handled by multiplying the factors.
- Here the tax is charged on the increment alone, so the overall factor is 1 + 0·20 + 0·05 × 0·20 = 1·21.
- The original price is therefore 1,331 ÷ 1·21 = ₹ 1,100, and the arithmetic is clean because 1,331 = 11³ and 1·21 = 1·1².
- Forward check: ₹ 1,100 rises by ₹ 220 to ₹ 1,320, tax of 5% on ₹ 220 is ₹ 11, and the customer pays ₹ 1,331.
- Had the tax been charged on the whole increased price the factor would have been 1·20 × 1·05 = 1·26, giving about ₹ 1,056 — a value not offered.
- To reverse a percentage increase, divide by the multiplier; subtracting the same percentage from the final amount is not the inverse operation.
- A rise of 20% followed by a fall of 20% leaves 96% of the original, which is the clearest demonstration that the two bases differ.
Study next
Common traps
- Charging the tax on the whole increased price when the stem charges it on the increment alone.
- Subtracting a percentage from the final amount instead of dividing by the multiplier to reverse a rise.
- Seeing a recognisable number such as 1,331 and inferring a process — eleven cubed does not mean three rises of ten per cent.
- Rounding a working figure early, which on a percentage item can move the result past a neighbouring option.
- Skipping the forward check, which on this item costs about ten seconds and would reject three of the four options.
Percentage items in EPFO papers come in three recognisable shapes. The first gives the final amount and asks for the original, as here, and is answered by dividing by the multiplier. The second gives the original and a chain of changes and asks for the final amount or the net percentage effect. The third embeds the percentage in a commercial setting — a discount, a profit, a tax, a commission — and tests whether the candidate can identify the base each rate is applied to. All three yield to the same two habits: build the multiplier from the words before touching the numbers, and then run the answer forwards through the story to confirm it. Papers also like to place a second percentage item close by in another guise, as this one does at question 108 with a discount and at question 112 with a percentage of a percentage.
Related PYQs
EPFO_APFC_2016_Q33In a medium-size township, the trend of annual immigration is an addition of 20% of the population as it was at the beginning; also 15% of the population as it was at the beginning is estimated to relocate elsewhere every year. If the current population is 80000, what is the likely population three years hence ?
- (a) 90000
- (b) 91200
- (c) 92000
- (d) 92610
Answer(d) 92610
The multiplier method over several periods — a township gaining 20% and losing 15% of its opening population each year, worked forward instead of backward.
EPFO_APFC_2016_Q94For which time intervals, is the percentage rise of population the same for the following data ? Period | Population 1970 | 40,000 1980 | 50,000 1990 | 60,000 2000 | 72,000 2010 | 80,000
- (a) 1970 – 80 and 1980 – 90
- (b) 1980 – 90 and 1990 – 2000
- (c) 2000 – 2010 and 1990 – 2000
- (d) 1980 – 90 and 2000 – 2010
Answer(b) 1980 – 90 and 1990 – 2000
Percentage change read off a table of populations, where the discipline being tested is again which figure is the base.
Practice
- practice — not a real PYQ
The price of an article is increased by 25%, and a tax of 4% is then charged on the increase alone. If the customer pays ₹ 1,260, what was the price of the article before the increase?
- (a)₹ 950
- (b)₹ 1,000
- (c)₹ 1,050
- (d)₹ 1,100
Answer(b) ₹ 1,000
- practice — not a real PYQ
The price of a commodity is raised by 10%, and the raised price is later raised by a further 10%. The overall increase over the original price is
- (a)20%
- (b)21%
- (c)22%
- (d)25%
Answer(b) 21%