Three varieties of rice costing ₹40/kg, ₹50/kg, and a third unknown price are mixed in the ratio 2 : 3 : 5. If the resulting mixt…

Question

Three varieties of rice costing ₹40/kg, ₹50/kg, and a third unknown price are mixed in the ratio 2 : 3 : 5. If the resulting mixture is sold at ₹55/kg, making a profit of 10% on the cost price, what is the price of the third variety of rice per kg?

1. A. ₹52.50
2. B. ₹57.50
3. C. ₹54.00 (Correct answer)
4. D. ₹62.50

Correct Answer

Option C — ₹54.00

Detailed Solution & Explanation

The correct answer is ₹54.00.

Key Points

• Convert the selling price back to the mixture's cost price: a 10% profit on selling at ₹55 means CP = 55 ÷ 1.1 = ₹50 per kg.
• Let the third variety cost x. With quantities in the ratio 2 : 3 : 5 over 10 parts:
  • (2 × 40 + 3 × 50 + 5x) ÷ 10 = 50
  • 80 + 150 + 5x = 500 → 5x = 270 → x = ₹54

Additional Information

• With three or more ingredients the weighted-average equation is the reliable route; classic two-ingredient alligation does not extend directly to three.
• Always convert the selling price to a cost price before averaging — mixing on the selling price is the commonest error in this question type.
• Check: (80 + 150 + 270) ÷ 10 = 500 ÷ 10 = ₹50 per kg, which sold at ₹55 gives exactly 10% ✓.

प्रश्न (हिन्दी में)

चावल की तीन किस्मों, जिनकी कीमत ₹40/किग्रा, ₹50/किग्रा तथा एक तीसरी अज्ञात कीमत है, को 2 : 3 : 5 के अनुपात में मिलाया जाता है। यदि परिणामी मिश्रण को ₹55/किग्रा पर बेचा जाता है, तो लागत मूल्य पर 10% का लाभ होता है, चावल की तीसरी किस्म का प्रति किग्रा मूल्य क्या है?

1. A. ₹52.50
2. B. ₹57.50
3. C. ₹54.00
4. D. ₹62.50