How many approximate kgs of sugar costing ₹45 per kg must be mixed with 25 kg of sugar costing ₹32 per kg so that a 15% gain may…

Question

How many approximate kgs of sugar costing ₹45 per kg must be mixed with 25 kg of sugar costing ₹32 per kg so that a 15% gain may be obtained by selling the mixture at ₹43.70 per kg?

1. A. 15 kg
2. B. 25 kg
3. C. 21 kg (Correct answer)
4. D. 18 kg

Correct Answer

Option C — 21 kg

Detailed Solution & Explanation

The correct answer is 21 kg.

Key Points

• Work backwards from the selling price to the mixture's cost. A 15% gain on selling at ₹43.70 means:
  • Cost of mixture = 43.70 / 1.15 = ₹38 per kg
• Now apply alligation between ₹32 and ₹45 to reach ₹38:
  • Cheaper : dearer = (45 − 38) : (38 − 32) = 7 : 6
• The ₹32 sugar is the 7-part share and weighs 25 kg, so one part = 25/7.
• The ₹45 sugar = 6 × 25/7 = 150/7 ≈ 21.4 kg, i.e. approximately 21 kg.
• Always convert the selling price to a cost price before alligating — mixing on the selling price is the commonest error in this question type.

Additional Information

• Alligation finds the ratio in which two ingredients at different prices are mixed to reach a given mean: cheaper : dearer = (dearer − mean) : (mean − cheaper).
• The mean must be a cost price, so convert any selling price back using CP = SP / (1 + gain%) before alligating.
• The same rule solves mixtures of milk and water, alloys, and average-speed questions where two speeds are held for different distances.

प्रश्न (हिन्दी में)

₹45 प्रति किग्रा वाली चीनी के लगभग कितने किग्रा को ₹32 प्रति किग्रा वाली 25 किग्रा चीनी के साथ मिलाया जाना चाहिए ताकि मिश्रण को ₹43.70 प्रति किग्रा पर बेचकर 15% लाभ प्राप्त किया जा सके?

1. A. 15 किग्रा
2. B. 25 किग्रा
3. C. 21 किग्रा
4. D. 18 किग्रा