In a division sum, the divisor is 20 times the quotient and 8 times the remainder. If the remainder is 50, what is the dividend?

Appeared in: RRB Nsg. Superintendent-2026 (Shift -1st)

Explanation

The question provides the remainder and relationships to find the divisor and quotient.
First, calculate the divisor: It is 8 times the remainder, so Divisor = 8 × 50 = 400.
Next, calculate the quotient: The divisor (400) is 20 times the quotient, so Quotient = 400 / 20 = 20.
Finally, use the division algorithm: Dividend = (Divisor × Quotient) + Remainder.
Substitute the values: Dividend = (400 × 20) + 50 = 8000 + 50 = 8050.

Option A: This result (8150) would be obtained if the remainder was 150 instead of 50, leading to (400 × 20) + 150. It represents a calculation error.
Option C: This result (8100) might arise from a calculation error, such as incorrectly adding 100 as the remainder instead of 50, i.e., (400 × 20) + 100.
Option D: This result (7950) is obtained by incorrectly subtracting the remainder instead of adding it: (400 × 20) - 50. The division algorithm requires adding the remainder.

Visual 1: Flowchart - A flowchart illustrating the step-by-step process: Start with the given Remainder -> Use it to calculate the Divisor -> Use the Divisor to calculate the Quotient -> Combine all three using the division formula to find the Dividend.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Division Algorithm and its application in word problems as background academic context rather than a clinical decision trigger.
While this is a mathematical aptitude question, strong arithmetic skills are fundamental for nurses.
Nurses frequently perform calculations for medication dosages, IV fluid rates, and patient intake/output monitoring, where accuracy is critical for patient safety.
What if the divisor was 10 times the quotient and 4 times the remainder? The same logical steps would apply, but with different numbers. Divisor = 4 * 50 = 200. Quotient = 200 / 10 = 20. Dividend = (200 * 20) + 50 = 4050. This shows the importance of applying the method rather than memorizing answers.

How to Approach the Question

First, identify all the given information and relationships in the problem: Remainder = 50, Divisor = 8 × Remainder, and Divisor = 20 × Quotient.
Work backward from the known value. Use the remainder (50) to find the divisor.
Once the divisor is known, use it to find the quotient.
Recall the standard division formula: Dividend = (Divisor × Quotient) + Remainder.
Substitute the calculated values of the divisor, quotient, and the given remainder into the formula.
Perform the arithmetic to find the final value of the dividend and match it with the options.

Concept Tested & Keywords

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Practise the full RRB Nsg. Superintendent-2026 (Shift -1st)

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