Question

In a ship there was stock of food for 200 days for 2000 persons. After 30 days, 1000 persons left the ship. For how may days shall the left-over food last for the remaining persons?

• A. 200
• B. 300
• C. 400
• D. 500

Hint:

The shortcut for this type of problem is to set up a "before and after" equation. The value of the remaining provisions is the same in both scenarios. (Original Persons) \(\times\) (Remaining Days) = (New Persons) \(\times\) (New Days). Here: \( 2000 \times (200 - 30) = (2000 - 1000) \times D \). This simplifies to \( 2000 \times 170 = 1000 \times D \), which gives \( D = 340 \). Always trust your method; if the options don't match, there may be an error in the question itself.

Answer 1

The Correct Option is C

Step 1: Understanding the Problem
This is a problem involving work and time, where the "work" is consuming the stock of food. The total amount of food can be measured in "person-days".

Step 2: Key Formula or Approach
\begin{enumerate}
Calculate the total amount of food available initially.
Calculate the amount of food consumed in the first 30 days.
Calculate the remaining food stock.
Calculate how long the remaining food will last for the remaining number of people. \end{enumerate}
Step 3: Detailed Explanation
1. Calculate Total Food Stock:
The total amount of food is enough for 2000 persons for 200 days. \[ \text{Total Food} = 2000 \text{ persons} \times 200 \text{ days} = 400,000 \text{ person-days} \] 2. Calculate Food Consumed:
For the first 30 days, there were 2000 persons. \[ \text{Food Consumed} = 2000 \text{ persons} \times 30 \text{ days} = 60,000 \text{ person-days} \] 3. Calculate Remaining Food:
\[ \text{Remaining Food} = \text{Total Food} - \text{Food Consumed} \] \[ \text{Remaining Food} = 400,000 - 60,000 = 340,000 \text{ person-days} \] Alternative (Simpler) Method:
1. Focus on the remaining food from the start:
After 30 days have passed, the remaining food is enough to feed the original 2000 persons for the remaining \( 200 - 30 = 170 \) days.
So, the amount of food left is: \[ \text{Remaining Food} = 2000 \text{ persons} \times 170 \text{ days} = 340,000 \text{ person-days} \] 2. Calculate the number of remaining persons:
Initially, there were 2000 persons. 1000 persons left. \[ \text{Remaining Persons} = 2000 - 1000 = 1000 \text{ persons} \] 3. Calculate how long the food will last:
Now, we need to find out how many days (D) the remaining food will last for the remaining 1000 persons. \[ \text{Remaining Food} = \text{Remaining Persons} \times D \] \[ 340,000 = 1000 \times D \] \[ D = \frac{340,000}{1000} = 340 \text{ days} \]
Step 4: Final Answer (Based on Calculation)
Based on the numbers given in the question, the left-over food will last for 340 days.