Time and Work Question 1 - CAT 2025
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:
Step-by-Step Explanation
- Determine the total man-hours required per team:
- Team A: 5 members × 40 hours = 200 man-hours
- Team B: 8 members × 50 hours = 400 man-hours
- Team C: 10 members × 4 hours = 40 man-hours
- Assign a smart value for Total Work:
Let the total work be the LCM of 200, 400, and 40, which is 400 units.
- Calculate the hourly efficiency of a single member from each team:
- Efficiency of 1 member from Team A = 400/200 = 2 units/hour
- Efficiency of 1 member from Team B = 400/400 = 1 unit/hour
- Efficiency of 1 member from Team C = 400/40 = 10 units/hour
- Analyze the first 23 hours of work:
The initial group consists of 2 members from A, 3 from B, and 1 from C.
Combined Hourly Efficiency = (2 × 2) + (3 × 1) + (1 × 10) = 4 + 3 + 10 = 17 units/hour
Work done in 23 hours = 17 × 23 = 391 units
Remaining Work = 400 − 391 = 9 units
- Analyze the final 1 hour of work:
The member from Team C leaves. The remaining members from A and B continue.
Current Group Efficiency = (2 × 2) + (3 × 1) = 7 units/hour
In the final 1 hour, this existing group will complete:
7 units/hour × 1 hour = 7 units
Shortfall to clear in the last hour = 9 − 7 = 2 units
Since each member of Team B contributes exactly 1 unit/hour, covering a shortfall of 2 units in 1 hour requires 2 additional members from Team B.
Correct Option: B
💡 FundaMakers Tip:
When handling group dynamics where individuals within teams share identical productivity levels, anchor your solution around the Total Man-Hours constraint (M × H). Finding the product of a team's headcount and its standalone deadline gives you a universal benchmark. Taking the LCM of these team benchmarks converts abstract group rates into whole numbers, making the rest of the problem simple arithmetic.