A liquid propellant technician mixes two batches of hydrazine fuels. Batch $A$ contains $80\%$ pure hydrazine and Batch $B$ contains $50\%$ pure hydrazine. In what ratio by volume should Batch $A$ and Batch $B$ be blended to produce a mixture containing $72\%$ pure hydrazine?

(A) 11 : 4

(B) 7 : 2

(C) 4 : 11

(D) 3 : 2

Answer Key:

Verified in official key

### 1. Strategy & Theoretical Principles By the standard Rule of Alligation: $$\frac{V_A}{V_B} = \frac{C_{\text{mix}} - C_B}{C_A - C_{\text{mix}}}$$ where: - $C_A = 80\%$ (concentration of higher component) - $C_B = 50\%$ (concentration of lower component) - $C_{\text{mix}} = 72\%$ (mean target concentration). ### 2. Analytical Formulation & Calculation $$\frac{V_A}{V_B} = \frac{72 - 50}{80 - 72} = \frac{22}{8} = \frac{11}{4}$$ Thus, Batch $A$ and Batch $B$ must be blended in the volumetric ratio of $11 : 4$. ### 3. Distractor Forensics - **Option A (11 : 4):** Correct alligation ratio. - **Option B (7 : 2):** Erroneous subtraction. - **Option C (4 : 11):** Inverted ratio (Batch B to Batch A). ### 4. Exam Trap & Standard Reference - **Trap Alert:** Always subtract the mean from the higher concentration in the denominator, and the lower from the mean in the numerator. - **Standard Reference:** Aggarwal, R.S., *Quantitative Aptitude*.

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