A vessel contains a mixture of apple, orange and mango juices in the ratio 5 : 12 : 8 respectively. 25 litres of the mixture is taken out, and 8 litres of apple juice and 4 litres of orange juice are added to the vessel. If the resulting quantity of apple juice is 10 litres less than the resulting quantity of orange juice, what was the initial quantity (in litres) of the mixture in the vessel?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 75
Let the vessel hold \(5k\), \(12k\) and \(8k\) litres of the three juices, \(25k\) litres in all. The 25 litres taken out are in the same ratio 5 : 12 : 8, that is 5, 12 and 8 litres.
Apple left \(=5k-5\), orange left \(=12k-12\)
After the additions: apple \(=5k-5+8=5k+3\), orange \(=12k-12+4=12k-8\)
Orange \(-\) apple \(=10\): \((12k-8)-(5k+3)=10\)
\(7k-11=10\), so \(k=3\)
Initial quantity \(=25\times3=75\) litres
The vessel held 75 litres at first.