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 $= 21600 + 17280 = \mathbf{38400}$.
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