Question

Arun, Tarun and Varun work for 24, 21 and 15 days respectively and get paid 2160, 2400 and 2160 rupees respectively. They get paid the same even if they work for a partial day. If the work has to be completed within 10 days or less, what is the minimum amount that has to be paid to complete the entire task?

Hint:

In work-wage problems, always find the 'cost per unit of work' for each worker to determine the most economical choice for completing the task.

Answer 1

Correct Answer: 2160

Step 1: Convert each person's terms into a "cost to complete the full job by that person" figure: Rs. \(2160\) for Arun, Rs. \(2400\) for Tarun, Rs. \(2160\) for Varun (each is just their quoted total pay, since wage and work-rate scale together). Tarun is visibly the most expensive per unit of work done.
Step 2: Check if skipping Tarun entirely still meets the deadline: Arun + Varun's combined rate is \(\tfrac1{24}+\tfrac1{15}=\tfrac{13}{120}\) of the job per day, giving a completion time of \(\tfrac{120}{13}\approx9.23\) days, comfortably under \(10\).
Step 3: Any split of the job between Arun and Varun alone costs exactly Rs. \(2160\) in total, since both have the same per-unit-work cost, whereas bringing in any amount of Tarun's work only adds cost at a higher rate (Rs. \(2400\) per full unit) without being necessary to meet the deadline.
Step 4: So the minimum achievable payment is \[ \boxed{\text{Rs. }2160} \]