A container holds a mixture of Orange, Apple, and Guava juices in the ratio of 5:7:4 respectively. 24 litres of this mixture is taken out, and then 10 litres of orange juice and 6 litres of guava juice are added to the vessel. If the resultant quantity of apple juice is 14 litres more than the resultant quantity of orange juice, what was the initial quantity of mixture in the vessel (in litres)?

Correct — A.
Let the vessel hold 16k litres: orange 5k, apple 7k, guava 4k.
24 L taken out in 5 : 7 : 4: orange 7.5 L, apple 10.5 L, guava 6 L.
After adding 10 L of orange: orange = 5k − 7.5 + 10 = 5k + 2.5

Apple, untouched by the additions: 7k − 10.5
Apple − orange = 14: (7k − 10.5) − (5k + 2.5) = 14
2k − 13 = 14, so k = 13.5
Initial quantity: 16 × 13.5 = 216 L → option (a)

Why the others are wrong

• (b)
  210 — 210 L gives k = 13.125, so apple ends at 81.375 L and orange at 68.125 L: a gap of 13.25 L, not 14.
• (c)
  214 — 214 L gives k = 13.375 and a final apple–orange gap of 2 × 13.375 − 13 = 13.75 L, just short of the 14 L the stem states.
• (d)
  235 — 235 L gives k = 14.6875 and a final apple–orange gap of 16.375 L, above the 14 L required.

Taking liquid out of a mixture removes each juice in the mixture's own ratio, so 24 L carries 24 × 5⁄16 = 7.5 L of orange and 24 × 7⁄16 = 10.5 L of apple.

Only the apple–orange gap enters the condition. Guava is removed and topped up, but it never appears in the equation.

Key facts

• Liquid drawn from a well-mixed vessel leaves in the vessel's current ratio.
• Here the final apple–orange gap is 2k − 13 litres when the vessel starts with 16k litres.
• 216 L in the ratio 5 : 7 : 4 is 67.5, 94.5 and 54 litres.

Common traps

• Taking all 24 L out of one juice instead of splitting it 7.5 : 10.5 : 6.
• Answering with the quantity after the changes, 216 − 24 + 16 = 208 L, when the stem asks for the initial quantity.
• Stopping at k = 13.5 and forgetting to multiply by the 16 parts.

No directly related past PYQ was found.