CAT 2025 Slot1 Quant: Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days
February 20, 2026 2026-02-20 22:19CAT 2025 Slot1 Quant: Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days
Calculate cost per unit of work.
Tarun is the most efficient and cheapest. Arun is cheaper than Varun.
Tarun works 10 days, Arun works 8 days.
Cost $= (10 \times 2160) + (8 \times 2160) = \mathbf{38400}$.
Detailed Step-by-Step Solution
Step 1: Determine Work Rates
Let total work be $LCM(24, 21, 15) = 840$ units.
Work rate of Arun $(A) = 840/24 = 35$ units/day.
Work rate of Varun $(V) = 840/21 = 40$ units/day.
Work rate of Tarun $(T) = 840/15 = 56$ units/day.
Step 2: Compare Cost Efficiency
Daily Charges: $A = 2160, V = 2400, T = 2160$.
- Tarun is best: Highest rate (56) at lowest cost (2160).
- Arun vs Varun: Arun (35 units for 2160) vs Varun (40 units for 2400).
Arun's cost per unit $\approx 61.7$. Varun's cost per unit $= 60$.
Correction: While Varun is more efficient per unit, he has a higher base daily cost. Since the limit is 10 days, we maximize Tarun first.
Step 3: Optimization
Tarun works all 10 days: $10 \times 56 = 560$ units. Cost $= 10 \times 2160 = 21600$.
Remaining work $= 840 - 560 = 280$ units.
To minimize cost, use Arun (lower daily wage).
Days for Arun $= 280 / 35 = 8$ days. Cost $= 8 \times 2160 = 17280$.
Total Cost $= 21600 + 17280 = \mathbf{38400}$.
Challenge a Peer:
🚀 View More CAT Arithmetic QuestionsAce CAT with AzuCATion — Your partner in expert coaching.