Time and Work Question 3 - CAT 2025
Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs. 2160, Rs. 2400, and Rs. 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is:
Step-by-Step Explanation
- Evaluate individual total job values:
Calculate the total cost required if each person completed the entire task alone:
- Arun: 24 days × Rs. 2160/day = Rs. 51,840
- Varun: 21 days × Rs. 2400/day = Rs. 50,400
- Tarun: 15 days × Rs. 2160/day = Rs. 32,400
- Apply the optimization strategy:
Tarun is the most cost-effective worker overall (Rs. 32,400 for the entire job). However, he requires 15 days, which violates the maximum allowed timeframe of 10 days.
To minimize the final cost, employ Tarun for the absolute maximum allowable limit of 10 days.
Work completed by Tarun in 10 days = 10/15 = 2/3 of the task
Remaining Work = 1 − 2/3 = 1/3 of the task
- Allocate the remaining work economically:
Compare the cost of completing the remaining 1/3 of the task between the other two workers:
Arun's Cost for 1/3 work = 1/3 × 51,840 = Rs. 17,280
Varun's Cost for 1/3 work = 1/3 × 50,400 = Rs. 16,800
Varun provides the better remaining value.
Let us calculate the time Varun requires:
Days needed by Varun = 1/3 × 21 days = 7 days
Since they can work concurrently on any given day, Varun's 7 days fit within the 10-day limit.
- Calculate the minimum total cost:
Total Cost = (10 days × Rs. 2160) + (7 days × Rs. 2400)
= 21,600 + 16,800
= Rs. 38,400
Correct Option: A
💡 FundaMakers Tip:
When work rates are paired with financial costs, do not focus on daily wages alone. Evaluate the total project cost per individual to determine who offers the best value per unit of work. Once identified, maximize the utilization of that resource up to the time limit constraint, then plug the remaining shortfall with the next best alternative.