A juice vendor mixes water with pure orange juice. If he sells the mixture at the cost price of pure orange juice and makes a pro…

Question

A juice vendor mixes water with pure orange juice. If he sells the mixture at the cost price of pure orange juice and makes a profit of 20%, what is the ratio of water to pure orange juice in the mixture, respectively?

1. A. 1 : 4
2. B. 1 : 5 (Correct answer)
3. C. 4 : 1
4. D. 5 : 1

Correct Answer

Option B — 1 : 5

Detailed Solution & Explanation

The correct answer is 1 : 5.

Key Points

• The vendor sells the mixture at the cost price of pure juice, so all the profit comes from the free water he has added.
• If the water is w and the juice j, his cost covers only j while his revenue covers (w + j):
  • Profit % = (water / juice) × 100 = 20%
• So w/j = 20/100 = 1/5, giving water : juice = 1 : 5.

Additional Information

• The general result: when an adulterated mixture is sold at the pure article's cost price, profit % = (quantity of adulterant / quantity of pure article) × 100.
• Note that the ratio is taken against the pure article, not the whole mixture — water is 1/6 of the mixture but 1/5 of the juice, and confusing the two gives the wrong option.
• Check with numbers: 5 litres of juice costing ₹100 plus 1 litre of water sells as 6 litres at ₹20/litre = ₹120, a profit of ₹20 on ₹100 ✓.

प्रश्न (हिन्दी में)

एक जूस विक्रेता शुद्ध संतरे के जूस में पानी मिलाता है। यदि वह मिश्रण को शुद्ध संतरे के जूस के लागत मूल्य पर बेचता है और 20% का लाभ कमाता है, तो मिश्रण में पानी और शुद्ध संतरे के जूस का अनुपात क्रमशः क्या है?

1. A. 1 : 4
2. B. 1 : 5
3. C. 4 : 1
4. D. 5 : 1