To fill a bucket, 25 mugs of water are required. How many mugs of water will be required to fill the bucket if the capacity of the mug is reduced to two-fifths of its present capacity?

Appeared in: DSSSB - 29 August 2019 (Shift-1)

Explanation

The core concept is inverse proportion: if the capacity of the mug decreases, the number of mugs needed to fill the same volume must increase.
The capacity of the mug is reduced to a factor of 2/5 of its original size.
To find the new number of mugs, you must multiply the original number of mugs (25) by the reciprocal of the factor, which is 5/2.
Calculation: 25 × (5/2) = 125 / 2 = 62.5.
Therefore, 62.5 of the smaller mugs are required to fill the bucket.

Option A: This is incorrect. This value might be obtained through a miscalculation, possibly by incorrectly simplifying the fractions or rounding the result.
Option B: This is an incorrect calculation. It does not follow the principle of inverse proportion for the given values.
Option D: This result would be obtained if you incorrectly multiplied the original number of mugs by 2 (25 x 2 = 50), instead of multiplying by the correct reciprocal of 5/2.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Inverse Proportion as background academic context rather than a clinical decision trigger.
While this is a mathematics question, the principle of inverse proportion is critical in nursing for safe medication administration.
For example, if a medication's concentration is halved (e.g., from 100 mg/mL to 50 mg/mL), the volume required to deliver the same dose must be doubled. A nurse must be able to perform this calculation accurately.
What if? If the capacity of the mug was instead increased to twice its size (a factor of 2), the number of mugs required would be halved. New number = 25 / 2 = 12.5 mugs.

How to Approach the Question

First, read the question carefully to identify the relationship between the quantities involved (number of mugs and capacity of the mug).
Recognize that to fill a fixed volume, a smaller container will require more units, and a larger container will require fewer units. This is an inverse proportion.
Set up the initial equation: Total Volume = (Initial number of units) × (Initial capacity of one unit).
Set up the new equation: Total Volume = (New number of units) × (New capacity of one unit).
Equate the two expressions and substitute the known values to solve for the unknown variable.
Alternatively, use the shortcut: New Number = Old Number × (1 / factor of change in capacity).

Concept Tested & Keywords

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Practise the full DSSSB - 29 August 2019 (Shift-1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.