CAT 2025 Slot 3 QA Question 7

Multiple choice (+3 / −1) · Arithmetic · Time & Work · Try it, then check the answer and solution below.

CAT 2025 Slot 3QAArithmetic • Time & WorkModerate

Teams A, B, and C consist of five, eight, and ten members, respectively, such that every member within a team is equally productive. Working separately, teams A, B, and C can complete a certain job in 40 hours, 50 hours, and 4 hours, respectively. Two members from team A, three members from team B, and one member from team C together start the job, and the member from team C leaves after 23 hours. The number of additional member(s) from team B, that would be required to replace the member from team C, to finish the job in the next one hour, is

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Official Convenor Answer Key: C

Answer and solution

Answer: C) 2

📌 Core Concept

The work rate of a team is the reciprocal of the time it takes to complete the job. For individual members, the work rate is the team's rate divided by the number of members. When teams work together, their rates add up.

🔢 Step-by-Step Solution

Calculate Work Rates per Member:

Team A:

\frac{1}{40} \div 5 = \frac{1}{200}

per hour

Team B:

\frac{1}{50} \div 8 = \frac{1}{400}

per hour

Team C:

\frac{1}{4} \div 10 = \frac{1}{40}

per hour

Initial Combined Work Rate (First 23 Hours):

2 members from A: $2 ×

\frac{1}{200}

CAT 2025 Slot 3 QA Question 7

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