Manish can complete a piece of work in 32 days. He worked for 4 days and then left. Satish completed the remaining work in 16 days. In how much time can Manish and Satish complete the work together?

Appeared in: RRB Nsg Superintendent -29 April 2025 (Shift-1st)

Explanation

The core of the problem is to find the individual work rates and then combine them.
Manish's 1-day work is 1/32. He works for 4 days, completing 4/32 = 1/8 of the work.
The remaining 7/8 of the work is completed by Satish in 16 days. This means Satish's 1-day work rate is (7/8) / 16 = 7/128.
Their combined 1-day work rate is the sum of their individual rates: 1/32 + 7/128.
To add the fractions, find a common denominator (128): 4/128 + 7/128 = 11/128.
The total time to complete the work together is the reciprocal of the combined rate: 1 / (11/128) = 128/11, which is 11 7/11 days.

Option A: This result would arise from an error in calculating the combined work rate or in the final division to convert the improper fraction.
Option B: This value might be obtained by miscalculating Satish's work rate or making a mistake while adding the fractions for the combined rate.
Option D: This is another incorrect value that likely results from a simple arithmetic mistake at some stage of the calculation, such as finding the LCM or adding the numerators.

Visual 1: Flowchart - A flowchart illustrating the step-by-step calculation: 1. Calculate Manish's work done. 2. Find remaining work. 3. Determine Satish's work rate. 4. Combine rates. 5. Calculate total time.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time Calculation as background academic context rather than a clinical decision trigger.
This type of problem tests logical reasoning and the ability to break down a task into measurable units (work rates), a skill useful for planning and resource management.
Understanding how to manipulate fractions and calculate rates is a fundamental mathematical skill applicable in various quantitative reasoning scenarios.
What if Satish took 21 days to finish the remaining work? Then Satish's rate for the whole work would be 21 / (7/8) = 24 days. His 1-day work would be 1/24. The combined work would be 1/32 + 1/24 = (3+4)/96 = 7/96. The total time would be 96/7 or 13 5/7 days.

How to Approach the Question

Identify the question type: This is a classic 'Work and Time' problem.
First, determine the rate of work for each individual. The rate is the amount of work done in one unit of time (e.g., 1 day).
Calculate the amount of work completed by the first person (Manish) and then determine the remaining work.
Use the remaining work and the time taken by the second person (Satish) to find their individual work rate.
Add the individual rates to find the combined rate of work.
The total time taken to complete the work together is the reciprocal of the combined rate. Convert the final fraction to a mixed number if required.

Concept Tested & Keywords

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Practise the full RRB Nsg Superintendent -29 April 2025 (Shift-1st)

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