Due to water crisis, $15%$ of the initial population left a town, and $60%$ of the remaining left the town for pursuing jobs. If 3400 people currently inhabit the town, what is the ratio of initial population to present population?

1. A

   56:22

2. B

   50:17

3. C

   55:24

4. D

   52:18

Appeared in: RRB Nsg. Superintendent -29 April-2025 (shift-2nd)

Explanation

• Let the initial population be P. After a 15% decrease, the remaining population is 0.85P.
• A further 60% decrease of the remaining population means 40% of that group stays. The final population is 0.40 * 0.85P = 0.34P.
• The ratio of the initial population (P) to the present population (0.34P) is P : 0.34P.
• To simplify the ratio, divide both sides by P, which gives 1 : 0.34.
• Multiplying by 100 to remove the decimal gives 100 : 34.
• Dividing both parts by their greatest common divisor (2) simplifies the ratio to 50 : 17.

Why Other Options Were Wrong

• Option A: This ratio (56:22) simplifies to 28:11, which does not match the calculated ratio of 50:17. This likely results from a calculation error.
• Option C: This ratio (55:24) is incorrect. It may arise from misinterpreting the percentages or errors in simplification.
• Option D: This ratio (52:18) simplifies to 26:9. This is not the correct ratio and stems from incorrect calculation of the remaining population.

Related Visual

• Visual 1: Flowchart - A flowchart illustrating the step-by-step reduction in population. Initial Population (100%) → Minus 15% → Remaining Population (85%) → Minus 60% of Remainder → Final Population (34%).

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating ratios based on successive percentage changes as background academic context rather than a clinical decision trigger.
• This question tests basic numeracy and aptitude, which is a fundamental skill for nurses.
• Nurses frequently use percentage and ratio calculations for tasks such as preparing medication dosages, calculating IV drip rates, and interpreting lab results.
• A strong grasp of these mathematical concepts is crucial for patient safety to prevent medication errors.

How to Approach the Question

• First, identify that this is a problem of successive percentage change. The second percentage is calculated on the new value, not the original one.
• Assume the initial population is a convenient number like 100 (or 'P').
• Calculate the population after the first decrease: 100 * (1 - 0.15) = 85.
• Calculate the final population by applying the second decrease to the new amount: 85 * (1 - 0.60) = 85 * 0.40 = 34.
• Form the ratio of the initial value to the final value: Initial : Final = 100 : 34.
• Simplify the ratio by dividing both numbers by their greatest common divisor (2) to get 50 : 17.

Concept Tested & Keywords

• Concept Tested: Calculating ratios based on successive percentage changes.
• Stem keywords: water crisis, population, 15%, 60%, remaining, 3400 people, ratio, initial population
• Lead-in keywords: what is the ratio

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