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In a vessel, there is a mixture of apple, orange and mango juices in the ratio of 3: 5: 4 respectively. A quantity of 12 litres from the mixture is replaced by 8 litres of apple juice. Thereafter the quantities of apple and orange juices in the resultant mixture become same. Find out the initial quantity of mixture in the vessel. 
  • a)
    76 litres
  • b)
    65 litres
  • c)
    60 litres
  • d)
    80 litres
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
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Given data:
- The initial ratio of apple, orange, and mango juices in the mixture is 3:5:4
- A quantity of 12 litres from the mixture is replaced by 8 litres of apple juice
- After replacement, the quantities of apple and orange juices in the mixture become the same

Let's assume that the initial quantity of the mixture is x litres.

Calculation:
- The initial quantity of apple juice in the mixture = 3/12 * x = x/4 litres
- The initial quantity of orange juice in the mixture = 5/12 * x = 5x/12 litres
- The initial quantity of mango juice in the mixture = 4/12 * x = x/3 litres
- After the replacement, the new quantity of apple juice in the mixture = (x/4 - 12 + 8) = (x/4 - 4) litres
- The new quantity of orange juice in the mixture remains the same = 5x/12 litres
- Let's assume that the new quantity of the mixture is y litres
- As per the question, the quantities of apple and orange juices in the mixture become the same after replacement. Therefore,
- (x/4 - 4) = 5x/24
- Solving the above equation, we get x = 60 litres
- Therefore, the initial quantity of the mixture is 60 litres.

Hence, option (c) is the correct answer.
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In a vessel, there is a mixture of apple, orange and mango juices in the ratio of 3: 5: 4 respectively. A quantity of 12 litres from the mixture is replaced by 8 litres of apple juice. Thereafter the quantities of apple and orange juices in the resultant mixture become same. Find out the initial quantity of mixture in the vessel.a)76 litresb)65 litresc)60 litresd)80 litrese)None of theseCorrect answer is option 'C'. Can you explain this answer?
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