QB_AE_GA_004 Section Question Bank NAT · 2 Marks
General Aptitude • Quantitative Aptitude • Arithmetic & Numerical Estimation

A supersonic blowdown wind tunnel storage vessel is charged by two independent compressors, C1 and C2. Operating together, they can pressurize the tank to $50\text{ bar}$ in $30\text{ minutes}$. If compressor C1 operating alone takes $50\text{ minutes}$ to achieve the same pressure, how many minutes will compressor C2 take when operating alone?

Answer Key:
75

Step-by-Step Verified Solution

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Work-Rate Formulation:** Let $R_1 = 1/50$ tank/min and $R_2 = 1/T_2$ tank/min. 2. **Stage 2: Combined Rate:** $R_1 + R_2 = 1/30$. 3. **Stage 3: Computation:** $1/T_2 = 1/30 - 1/50 = (5 - 3)/150 = 2/150 = 1/75$. 4. **Stage 4: Result:** $T_2 = 75\text{ minutes}$.
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