Four vessels are kept on a table in a manner that their quantity keeps on becoming 3 times when measured from left towards right.`25%` of the first vessel, `30%` of the second vessel, `40%` of the third vessel and `20%`of the fourth vessel are empty. If all the four vessels are emptied into the fifth vessel, then the total quantity is what percent of total quantity of the four vessel?

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Determine the capacities of the vessels
Assume the capacity of the first vessel (A) is 1 unit. According to the problem, the capacities of the vessels increase threefold from left to right:
- Capacity of Vessel A = 1 unit
- Capacity of Vessel B = 3 units (3 times A)
- Capacity of Vessel C = 9 units (3 times B)
- Capacity of Vessel D = 27 units (3 times C)

### Step 2: Calculate the total capacity of the four vessels
Total capacity = Capacity of A + Capacity of B + Capacity of C + Capacity of D
= 1 + 3 + 9 + 27 = 40 units

### Step 3: Calculate the empty quantities in each vessel
- For Vessel A: 25% is empty
- Empty quantity = 25% of 1 = 0.25 units
- For Vessel B: 30% is empty
- Empty quantity = 30% of 3 = 0.9 units
- For Vessel C: 40% is empty
- Empty quantity = 40% of 9 = 3.6 units
- For Vessel D: 20% is empty
- Empty quantity = 20% of 27 = 5.4 units

### Step 4: Calculate the total empty quantity
Total empty quantity = Empty quantity in A + Empty quantity in B + Empty quantity in C + Empty quantity in D
= 0.25 + 0.9 + 3.6 + 5.4 = 10.15 units

### Step 5: Calculate the filled quantities in each vessel
Filled quantity in each vessel = Total capacity of the vessel - Empty quantity
- For Vessel A: Filled = 1 - 0.25 = 0.75 units
- For Vessel B: Filled = 3 - 0.9 = 2.1 units
- For Vessel C: Filled = 9 - 3.6 = 5.4 units
- For Vessel D: Filled = 27 - 5.4 = 21.6 units

### Step 6: Calculate the total filled quantity
Total filled quantity = Filled quantity in A + Filled quantity in B + Filled quantity in C + Filled quantity in D
= 0.75 + 2.1 + 5.4 + 21.6 = 30.85 units

### Step 7: Calculate the percentage of the total filled quantity with respect to the total capacity
Percentage = (Total filled quantity / Total capacity) × 100
= (30.85 / 40) × 100 = 77.125%

### Final Answer
The total quantity in the fifth vessel is **77.125%** of the total capacity of the four vessels.

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