In a battle 70% of the combatants lost an eye, 80% lost one leg,85% lost ear,90% an arm.If x% lost all the four organs. The minimum value of x is

Options

A. 0.25
B. 0.2
C. 0.3
D. 0.35

Answer

To solve the problem step by step, we will use the principle of inclusion-exclusion to find the minimum percentage of combatants who lost all four organs.

### Step 1: Define the total number of combatants
Assume the total number of combatants is 100. This simplifies our calculations since we can directly use percentages as counts.

### Step 2: Identify the number of combatants who lost each organ
- Combatants who lost an eye: 70% of 100 = 70
- Combatants who lost a leg: 80% of 100 = 80
- Combatants who lost an ear: 85% of 100 = 85
- Combatants who lost an arm: 90% of 100 = 90

### Step 3: Calculate the number of combatants who lost both an eye and an ear
Using the inclusion-exclusion principle:
- Total who lost an eye and an ear = (Number who lost an eye) + (Number who lost an ear) - (Total combatants)
- = 70 + 85 - 100 = 55

This means 55 combatants lost both an eye and an ear.

### Step 4: Calculate the number of combatants who lost an eye, ear, and leg
Now, we find the number of combatants who lost an eye, ear, and leg:
- Total who lost an eye, ear, and leg = (Number who lost an eye and an ear) + (Number who lost a leg) - (Total combatants)
- = 55 + 80 - 100 = 35

This means 35 combatants lost an eye, ear, and leg.

### Step 5: Calculate the number of combatants who lost all four organs
Now, we find the number of combatants who lost all four organs:
- Total who lost an eye, ear, leg, and arm = (Number who lost an eye, ear, and leg) + (Number who lost an arm) - (Total combatants)
- = 35 + 90 - 100 = 25

This means 25 combatants lost all four organs.

### Step 6: Calculate the percentage of combatants who lost all four organs
To find the percentage of combatants who lost all four organs:
- Percentage = (Number who lost all four organs / Total combatants) × 100
- = (25 / 100) × 100 = 25%

### Conclusion
The minimum value of x, which represents the percentage of combatants who lost all four organs, is **25%**.

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