A, B and C together can complete a piece of work in 2 days. If A alone can complete the same work in 6 days and B can do it in 12 days, then how many days will C take to complete thrice the same work?

Appeared in: NCL (Northern Coalfields Limited)-NO

Explanation

The core concept is to use work rates (the amount of work done per day). The rate is the reciprocal of the time taken.
The combined rate of A, B, and C is 1/2 of the work per day.
The individual rates for A and B are 1/6 and 1/12, respectively.
C's rate is found by subtracting A's and B's rates from the combined rate: 1/2 - (1/6 + 1/12) = 1/4.
If C completes 1/4 of the work per day, C takes 4 days to complete the whole work.
The question asks for 'thrice the work', so the final time is 3 * 4 = 12 days.

Option A: This value (36) is incorrect. It might be obtained by incorrectly multiplying B's time (12 days) by 3, i.e., 3 * 12 = 36. This wrongly uses B's time instead of C's calculated time.
Option C: This value (24) is incorrect. It could be a result of a calculation error, perhaps by incorrectly adding or multiplying the given numbers, such as 2 * 12.
Option D: This value (16) is incorrect. It does not correspond to any logical step in the calculation and is likely a random distractor.

Visual 1: Flowchart: A flowchart illustrating the step-by-step calculation process: Start with given times -> Convert to daily work rates -> Calculate C's work rate -> Calculate time for C to do 1x work -> Calculate time for 3x work.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time as background academic context rather than a clinical decision trigger.
This question tests quantitative aptitude, a key skill for competitive examinations.
The ability to break down a problem into smaller, manageable parts is crucial for logical reasoning and problem-solving in any field.
What if the question asked for half the work? The time taken would be (Time for one work) / 2, which is 4 / 2 = 2 days.

How to Approach the Question

First, identify the time taken by each individual or group as stated in the problem.
Convert these times into 'work rates'. The work rate is the fraction of work done in one unit of time (in this case, one day). It is calculated as 1 / (Total time taken).
Set up an equation using the work rates. Here, the equation is: (A's rate) + (B's rate) + (C's rate) = (Combined rate of A, B, C).
Solve the equation to find the unknown variable, which is C's work rate.
Once you have C's work rate, find the time C takes to complete one unit of work by taking the reciprocal of the rate (Time = 1 / Rate).
Read the question carefully for the final step. Here, it asks for 'thrice the work', so multiply the time for one unit of work by 3.

Concept Tested & Keywords

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