QB_PH_GA_014: Quantitative Aptitude

Pipe A can fill a tank in 12 hours, while Pipe B can fill the same tank in 15 hours. A drainage Pipe C can empty the full tank in 20 hours. If all three pipes are opened simultaneously when the tank is empty, how many hours will it take to fill the tank completely?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Tank Capacity Assignment**: Take total capacity as $\text{LCM}(12, 15, 20) = 60\text{ units}$. 2. **Individual Hourly Rates**: - Rate of A: $r_A = \frac{60}{12} = +5\text{ units/hour}$ - Rate of B: $r_B = \frac{60}{15} = +4\text{ units/hour}$ - Rate of C: $r_C = -\frac{60}{20} = -3\text{ units/hour}$ (Emptying) 3. **Combined Net Rate**: $r_{\text{net}} = r_A + r_B + r_C = 5 + 4 - 3 = 6\text{ units/hour}$ 4. **Total Time Required**: $T = \frac{\text{Total Capacity}}{r_{\text{net}}} = \frac{60\text{ units}}{6\text{ units/hour}} = 10\text{ hours}$ 5. **Official Answer**: 10.