T1 and T2 together complete a work in 35 days. T2 alone can complete the same work in 105 days. They took Rs 7500 to complete the work together. What will be the share of T1?

1. A

   Rs. 7200

2. B

   Rs. 6000

3. C

   Rs. 5000

4. D

   Rs. 5500

Appeared in: CIP Ranchi 2023

Explanation

• The fundamental principle is that wages are distributed in the ratio of the work done by each individual.
• Since both T1 and T2 work for the same duration (35 days), their earnings will be in the ratio of their individual efficiencies (work rate).
• The efficiency of T1 is calculated by subtracting T2's efficiency from their combined efficiency. (T1+T2)'s efficiency is 1/35 of the work per day, and T2's is 1/105.
• T1's efficiency is (1/35 - 1/105) = 2/105 of the work per day. T2's efficiency is 1/105.
• The ratio of their efficiencies is T1:T2 = (2/105) : (1/105), which simplifies to 2:1.
• Therefore, T1's share is (2/3) of the total wage: (2/3) * 7500 = Rs. 5000.

Why Other Options Were Wrong

• Option A: This amount is incorrect. It does not correspond to the calculated efficiency ratio of 2:1.
• Option B: This amount would imply T1's share is 4/5 of the total, meaning an efficiency ratio of 4:1.
• Option D: This amount does not align with the 2:1 efficiency ratio derived from the problem data.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Time and Work: Wage Distribution as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude, a non-nursing subject often included in nursing entrance examinations to assess problem-solving and mathematical reasoning skills.
• Strong analytical and calculation skills are essential for nurses in various clinical applications, such as medication dosage calculations, fluid balance monitoring, and interpreting lab results.
• What if T1 and T2 worked for different durations? If they worked for different numbers of days, their shares would be in the ratio of (Efficiency × Time worked). The total work done by each person would need to be calculated first.

How to Approach the Question

• First, identify the information given: time taken by (T1+T2) and time taken by T2 alone.
• The core task is to find the individual work rate (efficiency) of T1.
• Calculate the work done per day for (T1+T2) and for T2. The work rate is the reciprocal of the time taken (e.g., rate = 1/days).
• Subtract T2's daily work from the combined daily work to find T1's daily work.
• Establish the ratio of T1's daily work to T2's daily work. This is the efficiency ratio.
• Since they worked for the same duration, divide the total wage (Rs. 7500) in this efficiency ratio to find T1's share.

Concept Tested & Keywords

• Concept Tested: Time and Work: Wage Distribution
• Stem keywords: T1 and T2, complete a work, 35 days, 105 days, Rs 7500, share of T1
• Lead-in keywords: What will be
• Negative lead-in flag: false

Question ID

QW9wEX2MWXDuqboUyWctN4

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