CAT 2025 Slot 1 · Quant · Question 18

CAT 2025 Slot 1 previous year question on Time and Work, with the answer and a step-by-step solution.

Time and WorkArithmeticMultiple choiceMedium

Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge ₹2160, ₹2400, and ₹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 ₹, required to be paid for the entire task is

A
34400
B
38880
C
47040
D
38400

Pick an option, then check.

Answer & solution

Answer: Option D

Take the task as 840 units (the LCM of 24, 21 and 15).

Then the daily outputs are Arun 35, Varun 40 and Tarun 56 units.

What matters is cost per unit of work, not cost per day:

Arun \frac{2160}{35}\approx 61.7, Varun \frac{2400}{40}=60, Tarun \frac{2160}{56}\approx 38.6.

So we will try to finish as much work as possible from Tarun, then Varun, and Arun only if forced.

Tarun works all 10 days, doing 560 units for 10\times 2160=21600.

That leaves 840-560=280 units. Varun does 40 a day, so he needs 7 days — comfortably within the 10, working alongside Tarun — costing 7\times 2400=16800.

Arun is never worth hiring, since he costs more per unit than Varun. The total is 21600+16800=38400, that is ₹38400.

CAT 2025 Slot 1 · Quant · Question 18

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