MPSC 2023 Prelims Paper-I · Question 40 of 100

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).

• (1)35°C — 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.
• (2)37°C — 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.
• (3)39°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.

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.

The general science section of an MPSC paper always contains a few arithmetical items chosen so that the working is short and the knowledge required is one formula. They are among the most reliable marks in the paper, because the calculation cannot be disputed and the answer is either right or wrong, and for the same reason they are unforgiving of a slip. The efficient way to handle them is to do the arithmetic on paper rather than in the head — here two lines, a subtraction and a multiplication — and then to apply whatever independent check the situation offers. Questions involving the human body offer a particularly good check, because normal body temperature, normal pulse rate and normal blood pressure are all narrow, familiar ranges, and a converted value that falls outside them is almost certainly a mistake. Note also the shape of this option set. Two of the four options can be dismissed on physiological grounds alone, and the remaining two are only one degree apart, so the question is designed to give partial credit for reasoning and then to require the calculation anyway. That combination — a rough check that narrows the field followed by arithmetic that settles it — is the pattern of most of the numerical items in this section.

• To convert a Fahrenheit reading to Celsius, subtract 32 and then multiply by five ninths; the subtraction corrects for the different zero points of the two scales and the multiplication for the different size of their degrees.
• Water freezes at 0 degrees Celsius or 32 degrees Fahrenheit and boils at 100 degrees Celsius or 212 degrees Fahrenheit, so 100 Celsius degrees cover the same interval as 180 Fahrenheit degrees, which is the origin of the ratio five to nine.
• A temperature of 104 degrees Fahrenheit is 40 degrees Celsius, since 104 less 32 is 72 and five ninths of 72 is 40.
• Normal human body temperature is about 37 degrees Celsius, or about 98.6 degrees Fahrenheit, which provides an immediate check on the plausibility of any answer to a question about fever.
• The Kelvin scale uses the same degree size as the Celsius scale but places its zero at absolute zero, so a Kelvin value is the Celsius value plus about 273; the Celsius and Fahrenheit scales give equal numerical readings only at minus forty degrees.

• Reversing the order of the two operations, or subtracting 32 after rescaling instead of before, which is the commonest arithmetical failure in temperature conversion
• Choosing the most familiar number in the option set, such as the figure for normal body temperature, before the stem has been read for what it actually asks
• Estimating rather than calculating when two options lie only one degree apart, where no rough check can separate them
• Ignoring the physical context; a temperature question about a person carries its own sanity check in the narrow range of normal body temperature

Numerical questions in the MPSC general science section are deliberately light: a single formula, small numbers, and no more than two or three steps of arithmetic. Temperature conversion is a recurring example, and it is asked in both directions and occasionally with the Kelvin scale added. Related items include the point at which the Celsius and Fahrenheit scales agree, the fixed points used to define a scale, the range of a clinical thermometer and the distinction between heat and temperature. The commission usually dresses the question in an everyday situation — a fever, the weather, a cooking temperature — and that dressing is not decoration, because it supplies a check on the answer. Expect at least two of the four options to be eliminable by that check and the remaining two to be close enough together that the calculation must be carried out.

No directly related past PYQ was found.

• practice — not a real PYQ

  At which temperature do the Celsius and the Fahrenheit scales give exactly the same numerical reading ?

  • (a)0 degrees
  • (b)32 degrees
  • (c)Minus 40 degrees
  • (d)100 degrees

  Answer(c) Minus 40 degrees — setting the two readings equal in the conversion relation and solving gives minus forty, and it is the only temperature at which the scales agree, since they have different zeros and different degree sizes and therefore cross at exactly one point. At 0 degrees Celsius the Fahrenheit reading is 32, at 32 degrees Celsius it is 89.6, and at 100 degrees Celsius it is 212.

• practice — not a real PYQ

  Normal human body temperature is about 37 degrees Celsius. What is this on the Fahrenheit scale ?

  • (a)96.8 degrees
  • (b)98.6 degrees
  • (c)100.4 degrees
  • (d)102.2 degrees

  Answer(b) 98.6 degrees — converting from Celsius reverses the two steps used in the other direction: multiply by nine fifths and then add 32, so 37 multiplied by nine fifths is 66.6 and adding 32 gives 98.6. The other three figures correspond to 36, 38 and 39 degrees Celsius respectively, which is why they cluster so closely around the right answer and why the arithmetic has to be done rather than estimated.