CAT 2025 Question Paper | Quant Slot 1

CAT Questions

CAT 2025 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 18 : 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

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Video Explanation

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Explanatory Answer

Assume Total Work = 840 units (LCM of 24, 21, 15).

Arun's rate:
\(\frac{840}{24}=35\text{ units/day}\)
(Cost = Rs 2,160)

Varun's rate:
\(\frac{840}{21}=40\text{ units/day}\)
(Cost = Rs 2,400)

Tarun's rate:
\(\frac{840}{15}=56\text{ units/day}\)
(Cost = Rs 2,160)

Cost per unit of work (Value for money):

Tarun:
\(\frac{2160}{56}\approx Rs\ 38.57/\text{unit}\)
(Cheapest)

Varun:
\(\frac{2400}{40}=Rs\ 60.00/\text{unit}\)

Arun:
\(\frac{2160}{35}\approx Rs\ 61.71/\text{unit}\)
(Most expensive)

As Tarun gives the best value, employ Tarun for the maximum limit of 10 days.

Tarun works for 10 days:
Work done \(=10\times56=560\) units
Cost \(=10\times2160=Rs\ 21,600\)

Finish remaining 280 units using Varun (as Varun is cheaper than Arun):
Remaining Work \(=840-560=280\) units
Days needed for Varun \(=\frac{280}{40}=7\) days
Cost \(=7\times2400=Rs\ 16,800\)

Total Cost \(=21,600+16,800=Rs\ 38,400\)

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The answer is '38400'

Choice 4 is the correct answer.

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