Two numbers are in the ratio 2:3. If 10 is subtracted from each of the numbers, the ratio becomes 3:5. Find the bigger number.

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

Explanation

Let the two numbers be 2x and 3x, based on the initial ratio of 2:3.
When 10 is subtracted from each, the new numbers are (2x - 10) and (3x - 10).
The problem states this new ratio is 3:5, leading to the equation: (2x - 10) / (3x - 10) = 3/5.
Solving for x by cross-multiplying: 5(2x - 10) = 3(3x - 10) which simplifies to 10x - 50 = 9x - 30, giving x = 20.
The original numbers are 2x = 2(20) = 40 and 3x = 3(20) = 60.
The question asks for the bigger of the two numbers, which is 60.

Option A: This value is incorrect and does not satisfy the conditions of the problem. It likely arises from a calculation error during the cross-multiplication or solving stage.
Option B: This is the value of the common multiplier 'x', not one of the actual numbers. A common mistake is to solve for 'x' and forget to substitute it back to find the numbers.
Option D: This is the smaller of the two numbers (2x = 2 * 20 = 40). The question specifically asks for the bigger number.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving linear equations derived from ratio and proportion problems as background academic context rather than a clinical decision trigger.
Ratio and proportion are fundamental math skills essential for safe nursing practice, particularly in medication dosage calculations and fluid management.
For example, if a medication is available as 50 mg in 2 mL, a nurse uses ratios to calculate how many mL to administer for a prescribed dose of 25 mg (50mg/2mL = 25mg/x mL).
Proficiency in these calculations prevents medication errors and ensures patient safety.

How to Approach the Question

First, identify the core task: this is a word problem that can be solved using algebra based on ratios.
Translate the words into mathematical expressions. Represent the initial numbers using a single variable, such as 2x and 3x, based on the given ratio 2:3.
Apply the change described in the problem. Subtracting 10 from each number gives you new expressions: (2x - 10) and (3x - 10).
Set up an equation using the new ratio provided: (2x - 10) / (3x - 10) = 3/5.
Solve the resulting linear equation for 'x' by cross-multiplying.
Finally, re-read the question carefully to ensure you are answering what is being asked. The question asks for the 'bigger number' (3x), not 'x' or the smaller number.

Concept Tested & Keywords

Concept Tested: Solving linear equations derived from ratio and proportion problems.
Stem keywords: ratio, 2:3, subtracted, 3:5, numbers
Lead-in keywords: Find the bigger number

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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.