80 multiplied by the square of a number gives the cube of 4 times the number. Find the number?

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

The problem requires translating a verbal statement into an algebraic equation.
Let the number be 'x'. The statement '80 multiplied by the square of a number gives the cube of 4 times the number' translates to the equation 80x² = (4x)³.
Solving the equation: 80x² = 64x³. Assuming x is not zero, we can divide by x², which gives 80 = 64x.
Isolating 'x' gives x = 80/64, which simplifies to 5/4 or 1.25.

Option A: If the number is 1, the left side of the equation is 80(1)² = 80, and the right side is (4×1)³ = 64. Since 80 is not equal to 64, this option is incorrect.
Option C: If the number is 0.8, the left side is 80(0.8)² = 51.2, and the right side is (4×0.8)³ = 3.2³ = 32.768. Since 51.2 is not equal to 32.768, this option is incorrect.
Option D: If the number is 1.2, the left side is 80(1.2)² = 115.2, and the right side is (4×1.2)³ = 4.8³ = 110.592. Since 115.2 is not equal to 110.592, this option is incorrect.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving algebraic equations derived from word problems as background academic context rather than a clinical decision trigger.
While this is a general mathematics problem, the core skill of solving for an unknown variable is fundamental in nursing for accurate medication dosage calculations, which is critical for patient safety.
Nurses frequently use formulas like (Desired Dose / Stock Strength) × Volume = Amount to Administer. This is a practical application of solving for an unknown.
What if? If the problem stated '4 times the cube of the number', the equation would be 80x² = 4(x³). Solving this would give x = 20, highlighting how critical precise translation from words to algebra is in high-stakes calculations.

How to Approach the Question

First, carefully read the problem to identify the unknown quantity and assign it a variable, such as 'x'.
Break down the problem into smaller phrases and translate each phrase into a mathematical expression. For example, 'square of a number' becomes x² and 'cube of 4 times the number' becomes (4x)³.
Combine these expressions into a single equation based on the relationship given in the problem: 80x² = (4x)³.
Solve the resulting equation for 'x'. Remember the order of operations and rules of exponents, such as (ab)ⁿ = aⁿbⁿ.
Simplify the equation (80x² = 64x³) and isolate 'x' to find its value (x = 80/64).
Convert the final fraction to a decimal if needed and compare your result with the given options.

Concept Tested & Keywords

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Practise the full DSSSB - 29 August 2019 (Shift-2)

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