Two numbers are in the ratio of 3:8. If the larger number is 40 more than smaller number, then the product of the numbers is:

Appeared in: OSSSC Nursing Officer-2023

Explanation

The numbers are in a 3:8 ratio, so they can be represented as 3x and 8x.
The problem states the difference between the numbers is 40, leading to the equation 8x - 3x = 40.
Solving the equation gives 5x = 40, which means x = 8.
The two numbers are therefore 3 * 8 = 24 and 8 * 8 = 64.
The product of these two numbers is 24 * 64, which equals 1536.

Option B: This is an incorrect product resulting from a calculation error. It does not logically follow from the problem's conditions.
Option C: This is an incorrect product resulting from a calculation error. It does not logically follow from the problem's conditions.
Option D: This is an incorrect product resulting from a calculation error. It does not logically follow from the problem's conditions.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving problems involving ratios and proportions as background academic context rather than a clinical decision trigger.
This type of ratio calculation is a foundational skill for safe medication administration in nursing.
Nurses use ratios and proportions daily to calculate drug dosages, IV drip rates, and solution concentrations, where a simple math error can have serious consequences.
What if? If the ratio was 2:7 and the difference was 50, the equation would be 7x - 2x = 50, leading to 5x = 50, so x = 10. The numbers would be 20 and 70, and the product would be 1400.

How to Approach the Question

First, identify the core mathematical concept, which is ratios.
Translate the word problem into algebraic expressions. Let the numbers be 3x and 8x based on the 3:8 ratio.
Formulate an equation based on the relationship described: 'the larger number is 40 more than the smaller number' translates to 8x - 3x = 40.
Solve the equation for the unknown variable 'x'.
Use the value of 'x' to find the actual values of the two numbers.
Finally, perform the requested operation, which is to find the product of the two numbers, and match the result to the options.

Concept Tested & Keywords

QIw49782upmkVbdGRsDAIq

Practise the full OSSSC Nursing Officer-2023

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