Question 1

Two containers have alcohol solutions of 20% and 50% concentration respectively. In what ratio should they be mixed to get a 35% solution?

Accepted Answer

Step 1: Use alligation method. Desired concentration = 35%. Step 2: Difference between 50% and 35% = 15 parts (from weaker solution). Step 3: Difference between 35% and 20% = 15 parts (from stronger solution). Step 4: Ratio = 15:15 = 1:1.

Question 2

A shopkeeper mixes two types of rice costing ₹40 per kg and ₹60 per kg in the ratio 3:2. At what price per kg should he sell the mixture to make a 25% profit?

Accepted Answer

Step 1: Cost of mixture per kg = (3×40 + 2×60)/(3+2) = (120 + 120)/5 = 240/5 = ₹48 per kg. Step 2: For 25% profit, selling price = 48 × 1.25 = ₹60 per kg.

Question 3

A chemist has two acid solutions: one with 30% acid and another with 60% acid. He mixes them in the ratio 2:3 and then adds 10 litres of pure water to the mixture. If the final solution has 36% acid, what was the original quantity of the 30% solution?

Accepted Answer

Step 1: Let 30% solution = 2x litres, 60% solution = 3x litres. Step 2: Acid from 30% solution = 0.30 × 2x = 0.6x litres. Step 3: Acid from 60% solution = 0.60 × 3x = 1.8x litres. Step 4: Total acid = 0.6x + 1.8x = 2.4x litres. Step 5: Total volume after adding water = 2x + 3x + 10 = 5x + 10 litres. Step 6: Final concentration: 2.4x/(5x + 10) = 0.36. Step 7: 2.4x = 0.36(5x + 10) → 2.4x = 1.8x + 3.6 → 0.6x = 3.6 → x = 6. Step 8: Original 30% solution = 2 × 6 = 12 litres.

RRB Group D Ratio & Proportion Questions

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