A and B together can do a piece of work in 10 days. A alone can do it in 30 days, the time in which B alone can do it is :

Appeared in: BSF Staff Nurse - 2021

Explanation

The problem requires finding the time B takes to complete a task alone, given the time taken by A alone and by A and B together.
The core principle is that work rates are additive. The rate of A and B working together is the sum of their individual rates.
First, calculate the work rates: (A+B)'s rate is 1/10 of the work per day, and A's rate is 1/30 per day.
Subtract A's rate from the combined rate to find B's rate: (1/10) - (1/30) = (3-1)/30 = 2/30 = 1/15.
A work rate of 1/15 means that B completes 1/15th of the work each day.
Therefore, the total time for B to complete the work is the reciprocal of the rate, which is 15 days.

Option A: 10 days is the time taken for A and B to complete the work together, not for B alone. This mistake arises from misreading the question's objective.
Option B: 12 days is an incorrect calculation. It does not logically follow from the standard work and time formulas.
Option D: 20 days is a common incorrect answer resulting from an arithmetic error. If one incorrectly calculates 1/10 - 1/30 as 1/20, this answer would be chosen. The correct calculation is 2/30.

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 and logical reasoning, which are essential skills for problem-solving in any field, including nursing.
While not a clinical question, the ability to perform calculations quickly and accurately is crucial for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data.
What if? If A could do the work in 20 days and A+B in 10 days, then A's rate is 1/20 and (A+B)'s rate is 1/10. B's rate would be 1/10 - 1/20 = 1/20, meaning B would take 20 days. This demonstrates how changing one variable affects the outcome.

How to Approach the Question

First, identify the question as a 'Work and Time' problem.
Recognize the key information provided: Time for (A+B) = 10 days, and Time for A = 30 days. The goal is to find the Time for B.
Convert the times into work rates. The rate is the reciprocal of the time (Rate = 1/Time). So, Rate(A+B) = 1/10 and Rate(A) = 1/30.
Set up the core equation: Rate(A) + Rate(B) = Rate(A+B).
Rearrange the equation to solve for the unknown: Rate(B) = Rate(A+B) - Rate(A).
Substitute the values and calculate: Rate(B) = 1/10 - 1/30. Find a common denominator to get (3-1)/30 = 2/30 = 1/15.

Concept Tested & Keywords

QSL1DoyJVkqIM7SPS-Shd7

Practise the full BSF Staff Nurse - 2021

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