A person spends 1/4 part of his salary on food, 3/8part of his salary on house rent. He is now left with Rs. 4,800. Find his total salary.

Appeared in: RRB Staff Nurse Kolkata-2015

Explanation

The total fraction of salary spent on food and house rent is calculated by adding the fractions: 1/4 + 3/8 = 5/8.
The remaining fraction of the salary is found by subtracting the spent fraction from the whole (1): 1 - 5/8 = 3/8.
This remaining fraction (3/8) is equal to the amount left, which is Rs. 4,800.
To find the total salary, we solve the equation: (3/8) × Total Salary = 4,800, which gives Total Salary = 4,800 × (8/3) = Rs. 12,800.

Option A: This result is obtained by incorrectly multiplying the remaining amount (Rs. 4,800) by the reciprocal of the spent fraction (8/5) instead of the reciprocal of the remaining fraction (8/3). The calculation would be 4,800 × (8/5) = 7,680.
Option B: This value does not logically follow from the fractions provided in the problem and represents a significant calculation error.
Option C: This amount (Rs. 9,600) is double the remaining amount (Rs. 4,800). This would only be correct if the remaining fraction of the salary was 1/2. However, the actual remaining fraction is 3/8.

Visual 1: Pie Chart - A pie chart showing the salary distribution: 2/8 (or 1/4) for food, 3/8 for house rent, and the remaining 3/8 (Rs. 4,800) as savings. This visually represents how the total salary is divided.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving word problems involving fractions to calculate a whole quantity from its parts as background academic context rather than a clinical decision trigger.
This type of problem tests foundational mathematical skills essential for various calculations in nursing, such as medication dosage, fluid balance, and data interpretation.
Accuracy in fraction and percentage calculations is a critical patient-safety skill to prevent errors in clinical practice.
What if? - If the person was left with Rs. 6,000 instead of Rs. 4,800, the total salary would be calculated as 6,000 × (8/3) = Rs. 16,000, demonstrating how the final answer changes proportionally with the remaining amount.

How to Approach the Question

First, identify the knowns: the fractions of salary spent (1/4 and 3/8) and the remaining amount (Rs. 4,800).
Calculate the total fraction of the salary that has been spent by adding the individual expense fractions. Find a common denominator to do this (1/4 + 3/8 = 2/8 + 3/8 = 5/8).
Determine the fraction of the salary that is left by subtracting the spent fraction from the whole (1). So, 1 - 5/8 = 3/8.
Set up an equation where the remaining fraction of the total salary (let's call it 'S') equals the remaining amount: (3/8) × S = 4,800.
Solve for 'S' to find the total salary: S = 4,800 × (8/3).
Check your answer against the given options.

Concept Tested & Keywords

Concept Tested: Solving word problems involving fractions to calculate a whole quantity from its parts.
Stem keywords: salary, spends, food, house rent, left with, Rs. 4,800
Lead-in keywords: Find his total salary

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