Anita can do 1/3 of a work in 5 days and Vinita can do 2/5 of work in 10 days. In how many days can they finish the work, if they work together?

Appeared in: ESIC Nursing Officer 2016 (Shift -2)

Explanation

The core of this problem is to determine the rate of work for each individual and then combine them.
First, calculate the total time each person would take to complete the work alone. Anita takes 15 days (5 days for 1/3 work) and Vinita takes 25 days (10 days for 2/5 work).
Next, express their work rates as fractions of the work done per day (Anita: 1/15, Vinita: 1/25).
Add their individual rates to find their combined rate of work: 1/15 + 1/25 = 8/75 of the work per day.
Finally, the total time to complete the work together is the reciprocal of their combined rate, which is 1 / (8/75) = 75/8 or 9 3/8 days.

Option B: This is an incorrect calculation. It might arise from rounding the final answer of 9.375 days down or from an error in adding the fractional work rates.
Option C: This is the time Vinita takes to complete 2/5 of the work. Choosing this answer reflects a misunderstanding of the question, which asks for the combined time to complete the entire work.
Option D: This is an incorrect calculation. There is no logical sequence of steps using the given numbers that results in 12. It likely stems from a calculation error, such as incorrectly finding the LCM or adding the fractions.

Visual 1: Flowchart: A flowchart can visually break down the problem-solving steps: 1. Calculate Anita's total time. 2. Calculate Vinita's total time. 3. Convert times to daily rates. 4. Add rates. 5. Invert the sum to find total days.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time Problems as background academic context rather than a clinical decision trigger.
This is a quantitative aptitude question designed to test mathematical reasoning and problem-solving skills.
While not directly related to clinical practice, the logical thinking and precision required are valuable skills for nurses in areas like medication dosage calculations and interpreting patient data.
What if Anita could do 1/2 of the work in 5 days? Her rate would be 1/10. The combined rate would be 1/10 + 1/25 = 7/50. The total time would be 50/7 or approximately 7.14 days, changing the answer.

How to Approach the Question

First, identify the information given for each person: the fraction of work completed and the time taken.
The key is to calculate the total time each person would take to complete 100% of the work alone. To do this, use the formula: Total Time = (Time Taken) / (Fraction of Work Done).
Once you have the total time for each person (e.g., Person A takes X days, Person B takes Y days), calculate their individual daily work rates. The rate is the reciprocal of the total time (Rate A = 1/X, Rate B = 1/Y).
Add the individual rates to find the combined daily work rate when they work together (Combined Rate = 1/X + 1/Y).
Finally, the time it takes for them to complete the work together is the reciprocal of the combined rate: Total Time Together = 1 / (Combined Rate).
Convert the final fraction to a mixed number if required by the options.

Concept Tested & Keywords

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Practise the full ESIC Nursing Officer 2016 (Shift -2)

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