The fever of a child is 104°F. What is this temperature in degree Celsius ?

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Correct — option (4), '40°C'. The conversion is a single formula: a Celsius reading equals the Fahrenheit reading less thirty-two, multiplied by five ninths. Applied here, 104 minus 32 is 72, and five ninths of 72 is 40, so the child's temperature is 40 degrees Celsius. The formula is worth understanding rather than merely memorising, because its two operations correspond to the two ways in which the scales differ. They differ first in where they put their zero: water freezes at 0 on the Celsius scale but at 32 on the Fahrenheit scale, so before any comparison of magnitudes can be made, the 32-degree head start has to be subtracted. They differ second in the size of a degree: between the freezing and boiling points of water the Celsius scale counts 100 degrees while the Fahrenheit scale counts 180, from 32 up to 212, so one Celsius degree is as large as 180 divided by 100, or nine fifths, of a Fahrenheit degree. Converting the other way therefore requires multiplication by five ninths. Subtract the offset, then rescale the degree — that is the whole of the method, and getting the order wrong is the commonest way to fail this arithmetic. The answer can also be checked without repeating the calculation. Normal human body temperature is about 37 degrees Celsius, which is about 98.6 degrees Fahrenheit, and the stem describes a fever, so the reading of 104 must convert to something comfortably above 37. That single observation eliminates two of the four options before any division is done and shows how a physical fact can police an arithmetical one. A temperature of 40 degrees Celsius is a high fever, which is consistent with the situation the stem describes, so the arithmetic and the physiology agree and the answer is option (4).

Why the other options are wrong — (a) Thirty-five degrees Celsius corresponds to 95 degrees Fahrenheit, not 104, so the arithmetic fails outright. It also fails a check that costs no time at all: 35 degrees Celsius is below normal body temperature, which is about 37, so a child at that temperature would be abnormally cold rather than feverish, and the stem states plainly that the child has a fever. This option is generally reached either by subtracting 32 and then dividing by something other than nine fifths, or by a candidate who is converting in the wrong direction and has multiplied where he should have divided. The lesson is that a temperature question about a human being always carries its own sanity check, because the plausible range of body temperature is narrow and well known, and any converted value outside it should be treated as a signal to redo the arithmetic.  (b) Thirty-seven degrees Celsius is normal human body temperature and corresponds to about 98.6 degrees Fahrenheit. Choosing it therefore contradicts the stem twice over: the arithmetic does not give it, and the stem says the child has a fever, which by definition means a temperature above the normal figure. The option exists because 37 is the number most strongly associated with body temperature in a candidate's memory, and under time pressure a familiar number can be selected before the question has been read properly. It is a useful reminder that the most recognisable option in a set is often placed there precisely because it is recognisable, and that recall of a related fact is not the same as an answer to the question asked.  (c) This is the most dangerous of the three wrong options, because 39 degrees Celsius is a perfectly plausible fever and survives every sanity check that eliminates the other two — it is above normal body temperature, it is within the range a clinical thermometer covers, and it sounds like a figure a doctor might quote. What it does not survive is the arithmetic: 39 degrees Celsius converts to 102.2 degrees Fahrenheit, not 104. The two candidate answers are adjacent, and no amount of estimating will separate them, which is exactly why the commission has placed them side by side. Where two options lie one unit apart, the sanity check has done all it can and the calculation must actually be performed; here the calculation is a subtraction and a multiplication by a simple fraction and takes only a few seconds.

Concept: Three temperature scales are in common use and they differ in two respects only: where the zero is placed and how large a degree is. The Celsius scale takes the freezing point of water as zero and its boiling point as 100, dividing the interval into a hundred equal parts. The Fahrenheit scale places the freezing point at 32 and the boiling point at 212, dividing the same physical interval into 180 parts, so its degree is smaller — nine Fahrenheit degrees span the same warming as five Celsius degrees. The Kelvin scale keeps the Celsius degree but moves the zero to absolute zero, the temperature at which the thermal motion of particles is at a minimum and below which nothing can be cooled, so a Kelvin reading is a Celsius reading plus about 273. Because the differences are only of origin and of unit, any conversion is a two-step affair: shift the zero, then rescale, and the relations are conveniently held in the single chain that sets the Celsius value over five equal to the Fahrenheit value less thirty-two over nine. Two particular readings are worth memorising as anchors. Normal human body temperature is about 37 degrees Celsius or 98.6 degrees Fahrenheit, which is why the clinical thermometer is graduated over a narrow range around that figure rather than over the whole scale. And minus forty is the single point at which the Celsius and Fahrenheit scales give the same numerical reading, the two scales crossing there and diverging on either side.

State PCS 2023 Q40 — Science & Technology PYQ with Answer

State PCS 2023 Q40 — Science & Technology PYQ with Answer