Two bottles of same capacity are `35%` and `33 1/3`% full of orange juice, respectively. They are filled up completely with apple juice and then the contents of both bottles are emptied into another vessel. The percentage of apple juice in the mixture is: /
समान धारिता वाले दो बोतल क्रमशः `35%` और `33 1/3`% संतरे के जूस से भरे हुए हैं | उन्हें पूरी तरह सेब के जूस से भर दिया जाता है तथा फिर दोनों बोतलों की सामग्रियों को एक अन्य बर्तन में उड़ेल दिया जाता है | इस मिश्रण में सेब के जूस का प्रतिशत कितना है ?

Options

A. `34 1/6`
B. `64 1/3`
C. `60 2/3`
D. `65 5/6`

Answer

To solve the problem, we need to find the percentage of apple juice in the mixture after combining the contents of two bottles filled with orange juice and then topped off with apple juice.

### Step-by-Step Solution:

1. **Determine the percentage of orange juice in each bottle:**
- Bottle 1: 35% orange juice
- Bottle 2: 33 1/3% orange juice (which can be converted to a fraction: 33 1/3% = 33.33% = 1/3)

2. **Convert the percentage of orange juice in Bottle 2 to a fraction:**
- 33 1/3% = 33.33% = 33.33/100 = 1/3 = 0.3333 (approximately)

3. **Calculate the average percentage of orange juice in the mixture:**
- Average percentage of orange juice = (Percentage in Bottle 1 + Percentage in Bottle 2) / 2
- Average percentage = (35% + 33 1/3%) / 2
- Convert 33 1/3% to a decimal: 33 1/3% = 33.33%
- Average percentage = (35 + 33.33) / 2 = 68.33 / 2 = 34.1667%

4. **Determine the percentage of apple juice in the mixture:**
- Total percentage = 100%
- Percentage of apple juice = 100% - Average percentage of orange juice
- Percentage of apple juice = 100% - 34.1667% = 65.8333%

5. **Convert the percentage of apple juice to a fraction:**
- 65.8333% can be expressed as 65 5/6% (since 0.8333 is approximately 5/6).

### Final Answer:
The percentage of apple juice in the mixture is **65 5/6%**.