Given that M : N = 5 : 4 & N : P = 4 : 7. If the difference between P and M is 11, find N.

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

Explanation

The problem requires combining two separate ratios that share a common term (N).
Since the value for N is identical (4) in both M:N and N:P, the ratios can be merged directly into M:N:P = 5:4:7.
A common multiplier 'x' is used to represent the actual values (M=5x, N=4x, P=7x).
The given difference (P - M = 11) allows for the creation of an algebraic equation (7x - 5x = 11).
Solving this equation yields x = 5.5.
The value of N is then found by substituting x into its expression (N = 4 * 5.5 = 22).

Option B: This value would be correct only if the common multiplier 'x' were 11.
Option C: This value would be correct only if the common multiplier 'x' were 16.5.
Option D: This is the value of the difference between P and M, not the value of N.

Visual 1: Flowchart: A flowchart illustrating the step-by-step process: 1. Write down given ratios. 2. Check for a common term and combine ratios. 3. Introduce a variable 'x'. 4. Use the given difference to form an equation. 5. Solve for 'x'. 6. Calculate the required value.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving problems involving combined ratios and proportions as background academic context rather than a clinical decision trigger.
This question tests basic mathematical aptitude, a non-nursing subject area that is part of many nursing entrance and recruitment examinations.
Strong numerical skills are essential for nurses for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data charts.
What if the ratios were M:N = 5:2 and N:P = 4:7? You would first need to make N common by multiplying the first ratio by 2, resulting in M:N = 10:4. Then you could combine them as M:N:P = 10:4:7 and proceed with the calculation.

How to Approach the Question

First, identify all the given information: two separate ratios (M:N and N:P) and a numerical relationship (P - M = 11).
Check if the common term in both ratios (N) has the same value. In this case, it is 4 in both, so you can combine them directly.
Create a single continuous ratio: M : N : P = 5 : 4 : 7.
Represent the actual values using a common multiplier, 'x' (M=5x, N=4x, P=7x).
Use the given numerical relationship (P - M = 11) to set up an equation: 7x - 5x = 11.
Solve the equation for 'x' and then substitute this value back into the expression for N to find the final answer.

Concept Tested & Keywords

Q87t9w9vlhavPrUcqjDY7O

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.