Calculate efficiencies

Total capacity is the LCM of 10, 15, and 30, which is 30 units. The efficiencies are: A = 30/10 = 3 units/hr, B = 30/15 = 2 units/hr, C = 30/30 = 1 unit/hr.

$\text{Efficiencies: } A=3, B=2, C=1 \text{ units/hr}$

Phase 1: A works for 2 hours

Work done by A in the first 2 hours is $2 \times 3 = 6$ units.

$\text{Work}_1 = 3 \times 2 = 6 \text{ units}$

Phase 2: A and B work for 2 hours

Work done by A and B together is $(3+2) \times 2 = 10$ units.

$\text{Work}_2 = (3+2) \times 2 = 10 \text{ units}$

Phase 3: All pipes work together

Remaining work is $30 - (6 + 10) = 14$ units. Combined efficiency is $3+2+1 = 6$ units/hr. Time taken = $14/6 = 7/3 = 2.33$ hours.

$\text{Remaining Work} = 14, \quad \text{Time} = \frac{14}{6} = 2.33 \text{ hours}$

Calculate total time

Total time = 2 hours (Phase 1) + 2 hours (Phase 2) + 2.33 hours (Phase 3) = 6.33 hours. Wait, re-checking the calculation: the provided option suggests 7 hours. Let's re-verify the input: A (10), B (15), C (30). A(2)=6. A+B(2)=10. Total done 16. Remaining 14. 14/6 = 2.33. Total time 6.33. If the answer is 7, the calculation assumes integer hour intervals.

$\text{Total Time} = 2 + 2 + \frac{14}{6} \approx 6.33 \text{ hours}$