Ramesh can complete a piece of work alone in 16 days and Suresh can complete the same piece of work alone in 4 days. They started the work together, but Ramesh had to leave 6 days before the completion of the work. In how many days will the work complete?

1. A

   4 5/6

2. B

   4 7/6

3. C

   4 5/6

4. D

   4 2/5

Appeared in: DSSSB 13 August 2024

Explanation

• The individual rates of work are calculated first: Ramesh's rate is 1/16 of the job per day, and Suresh's rate is 1/4 of the job per day.
• Let 'x' be the total number of days to complete the work. Since Ramesh leaves 6 days before completion, he works for (x - 6) days, while Suresh works for the entire duration 'x'.
• The total work is the sum of their individual contributions, which must equal 1 (the whole job). This gives the equation: (x - 6)/16 + x/4 = 1.
• Solving the equation involves finding a common denominator (16), which simplifies the equation to (x - 6) + 4x = 16.
• Combining terms gives 5x = 22, which leads to x = 22/5.
• Converting the improper fraction 22/5 to a mixed number gives 4 2/5 days.

Why Other Options Were Wrong

• Option A: This is an incorrect calculation. It may result from errors in setting up the initial equation, such as misinterpreting when Ramesh leaves.
• Option B: This is an incorrect calculation and an improperly formatted mixed fraction. The fraction part (7/6) is greater than 1, making the number equivalent to 5 1/6.
• Option C: This is a duplicate of the first option and is incorrect for the same reasons. It's a result of a calculation error.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving 'Time and Work' problems using algebraic equations as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude, a non-nursing subject crucial for passing the general aptitude section of nursing recruitment exams.
• The key skill is translating a word problem into a precise mathematical equation. A single misinterpreted phrase, like 'before completion' versus 'after starting', completely changes the equation.
• What if Ramesh left 6 days after they started working together? In that case, for the first 6 days, they work together. The work done would be 6 * (1/16 + 1/4). The remaining work would be completed by Suresh alone. This demonstrates how critical careful reading is.

How to Approach the Question

• First, identify the individual rates of work. The rate is the reciprocal of the time taken to complete the work alone (e.g., Rate = 1 / Time).
• Define a variable for the unknown quantity. Here, the unknown is the total number of days to complete the work, let's call it 'x'.
• Carefully read the conditions to determine how long each person worked. Suresh worked for the full 'x' days. Ramesh left 6 days before completion, so he worked for (x - 6) days.
• Set up the work equation: (Rate of Person 1 × Time of Person 1) + (Rate of Person 2 × Time of Person 2) = 1.
• Substitute the known values and expressions into the equation: (1/16) * (x - 6) + (1/4) * x = 1.
• Solve the resulting algebraic equation for 'x' and ensure the final answer is in the format required by the options (in this case, a mixed fraction).

Concept Tested & Keywords

• Concept Tested: Solving 'Time and Work' problems using algebraic equations.
• Stem keywords: complete a piece of work, alone in 16 days, alone in 4 days, work together, leave 6 days before completion
• Lead-in keywords: In how many days

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