A garrison is provided with ration for 72 soldiers to last for 54 days . Find how long would the same amount of food last for 90 soldiers, if the individual ration is reduced by 10% ?

Options

A. 48 days
B. 72 days
C. 54 days
D. 126 days

Answer

To solve the problem step by step, we will use the Unitary Method.

### Step 1: Calculate the total amount of food available.
The food is initially provided for 72 soldiers for 54 days.

Total food = Number of soldiers × Number of days
Total food = 72 soldiers × 54 days = 3888 soldier-days

**Hint:** Remember that "soldier-days" represents the total amount of food in terms of how many soldiers can be fed for how many days.

### Step 2: Calculate the effective ration per soldier after the reduction.
The individual ration is reduced by 10%.

If the original ration is considered as 100%, after a 10% reduction, the new ration per soldier is:
New ration = 100% - 10% = 90%

**Hint:** Think of the ration as a percentage of the original amount; reducing it by 10% means each soldier gets only 90% of the original ration.

### Step 3: Calculate the total food available for 90 soldiers with the reduced ration.
Now, we need to find out how long the same amount of food (3888 soldier-days) will last for 90 soldiers with the new ration.

Since each soldier now gets 90% of the original ration, the effective number of soldiers that can be fed with the same amount of food is:
Effective soldiers = 90 soldiers × (90/100) = 81 soldiers

**Hint:** When the ration is reduced, it effectively increases the number of soldiers that can be supported by the same total food.

### Step 4: Calculate how many days the food will last for 90 soldiers.
Now we can find out how many days the food will last for 90 soldiers:

Using the total food calculated earlier:
Days = Total food / Effective soldiers
Days = 3888 soldier-days / 81 soldiers = 48 days

**Hint:** This step involves dividing the total food by the number of effective soldiers to find out how many days the food will last.

### Conclusion
The same amount of food will last for 90 soldiers for **48 days**.

**Final Answer:** 48 days