A is twice as fast as B, and B is three times as fast as C. Together with D, all three complete a work in 17 days, and D alone can complete the same work in 36 days. A and C start the work and leave after 2 days. How many days will B take to complete three times the remaining work?

1. A

   3 दिन

2. B

   4 दिन

3. C

   308 2/19 दिन

4. D

   5 दिन

Appeared in: JSSH Staff Nurse - 2019

Explanation

• The core of the problem is to find the total work units, which is calculated as 6120/19 units.
• A and C, with a combined efficiency of 7 units/day, complete 14 units of work in 2 days.
• The remaining work is (6120/19) - 14 = 5854/19 units.
• The task for B is to complete three times this remaining work, which is 3 * (5854/19).
• Since B's efficiency is 3 units/day, the time taken is (3 * 5854/19) / 3, which simplifies to 5854/19 days.
• Converting the improper fraction 5854/19 to a mixed fraction results in 308 2/19 days.

Why Other Options Were Wrong

• Option A: This is an extremely small value and likely results from a major calculation error, possibly by incorrectly simplifying the efficiencies or the work units.
• Option B: Similar to the first option, this value is too small and indicates a significant miscalculation, perhaps by ignoring the fractional nature of the total work.
• Option D: This is another small integer value that does not align with the calculations involving fractions derived from the work rates (1/17 and 1/36).

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the ability to solve complex problems related to work and time, involving multiple individuals with varying efficiencies as background academic context rather than a clinical decision trigger.
• This question assesses general aptitude and problem-solving skills, which are essential for nurses in making quick, logical decisions and performing calculations (e.g., drug dosages, IV drip rates) accurately under pressure.
• What if? If the question asked for B to complete only the remaining work (not three times), the answer would be (5854/19) / 3 = 5854/57 days, which is approximately 102.7 days.

How to Approach the Question

• First, break down the relationships between the workers' speeds. Assign a base efficiency (e.g., C=1 unit/day) and calculate the efficiencies of the others based on this.
• Next, formulate an equation for the total work (W). Use the principle that Work = Rate × Time. The rate of a group is the sum of individual rates.
• Use the information about (A+B+C+D) working together and D working alone to find the combined rate of (A+B+C) in terms of W. Equate this to their combined efficiency (from step 1) to solve for W.
• Calculate the amount of work completed in the initial phase (A and C working for 2 days).
• Subtract the completed work from the total work to find the remaining work.
• Finally, calculate the time required for B to complete the specified multiple of the remaining work using the formula: Time = Work / Efficiency.

Concept Tested & Keywords

• Concept Tested: This question tests the ability to solve complex problems related to work and time, involving multiple individuals with varying efficiencies.
• Stem keywords: twice as fast, three times as fast, complete a work, remaining work, A and C start, B to complete
• Lead-in keywords: How many days

Question ID

QKpBQlPsH9YisHCVG562WX

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