In a division problem, the divisor is 17 times the quotient and 11 times the remainder. If the remainder is 34, what is the dividend?

Appeared in: RRB Nsg. Superintendent-2026 (Shift -3rd)

Explanation

The solution requires applying the fundamental division formula: Dividend = (Divisor × Quotient) + Remainder.
First, calculate the Divisor. The problem states the divisor is 11 times the remainder (34). So, Divisor = 11 × 34 = 374.
Next, calculate the Quotient. The problem states the divisor (374) is 17 times the quotient. So, Quotient = 374 ÷ 17 = 22.
Finally, calculate the Dividend using the formula: Dividend = (374 × 22) + 34.
Performing the multiplication and addition: 8228 + 34 = 8262.

Option A: This value is incorrect. It would result from an error in calculation, such as miscalculating the product of the divisor and quotient or using an incorrect remainder.
Option B: This value is incorrect. It is slightly higher than the correct answer and likely results from a minor arithmetic error during the final addition step.
Option C: This value is incorrect. It is slightly lower than the correct answer, suggesting a possible miscalculation, perhaps by subtracting the remainder instead of adding it.

Visual 1: Flowchart: A flowchart illustrating the step-by-step process: Start with Remainder -> Calculate Divisor -> Calculate Quotient -> Calculate Dividend. This visualizes the logical sequence of the calculation.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Relationship between Dividend, Divisor, Quotient, and Remainder as background academic context rather than a clinical decision trigger.
This question tests basic mathematical aptitude and logical reasoning, which are essential skills for nurses.
Nurses frequently use mathematical calculations for drug dosage, IV drip rates, and interpreting patient data. Accuracy is critical to ensure patient safety.
What if the remainder was 17 instead of 34? The divisor would be 11 × 17 = 187. The quotient would be 187 ÷ 17 = 11. The dividend would be (187 × 11) + 17 = 2057 + 17 = 2074.

How to Approach the Question

First, identify all the known values and relationships given in the word problem. Write them down as simple equations (e.g., Remainder = 34, Divisor = 11 × Remainder).
Identify the unknown value you need to find, which is the Dividend.
Recall the fundamental formula for division: Dividend = (Divisor × Quotient) + Remainder.
Work backward from the known value (Remainder) to find the other unknown components (Divisor, then Quotient) one by one.
Substitute all the calculated values back into the main formula to find the final answer.
Double-check your arithmetic at each step to avoid simple calculation errors.

Concept Tested & Keywords

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Practise the full RRB Nsg. Superintendent-2026 (Shift -3rd)

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