At a refugee camp, the food supplies were enough to feed 300 refugees for 45 days. But 60 more refugees joined after 15 days. For how many days would the rest of the food supplies last?
Understanding the Refugee Camp Food Supply Problem
This question involves a classic scenario of work and time, specifically dealing with how resources (food supplies) last for a changing number of people (refugees). We need to calculate how long the remaining food will last after the population increases.
Initial Food Supply Calculation
Initially, the food supplies were sufficient for 300 refugees for 45 days. We can think of the total amount of food as a certain number of "refugee-days" of consumption. If one refugee consumes one unit of food per day, the total initial food supply can be calculated as:
\(\text{Total Food Units} = \text{Number of Refugees} \times \text{Number of Days}\)
\(\text{Total Food Units} = 300 \times 45\)
\(\text{Total Food Units} = 13500 \text{ refugee-days}\)
Food Consumed in the First 15 Days
For the first 15 days, there were 300 refugees. The amount of food consumed during this period is:
\(\text{Food Consumed} = \text{Number of Refugees} \times \text{Number of Days}\)
\(\text{Food Consumed} = 300 \times 15\)
\(\text{Food Consumed} = 4500 \text{ refugee-days}\)
Calculating Remaining Food Supplies
After 15 days, we find the amount of food that is left by subtracting the consumed food from the total initial supply:
\(\text{Remaining Food Units} = \text{Total Food Units} - \text{Food Consumed}\)
\(\text{Remaining Food Units} = 13500 - 4500\)
\(\text{Remaining Food Units} = 9000 \text{ refugee-days}\)
Alternatively, we know the initial supply was for 300 refugees for 45 days. After 15 days, the supply is still enough for 300 refugees, but only for the remaining days (\(45 - 15 = 30\) days). So, the remaining food is:
\(\text{Remaining Food Units} = 300 \times (45 - 15)\)
\(\text{Remaining Food Units} = 300 \times 30\)
\(\text{Remaining Food Units} = 9000 \text{ refugee-days}\)
Determining the New Number of Refugees
After 15 days, 60 more refugees joined the camp. The new total number of refugees is:
\(\text{New Total Refugees} = \text{Initial Refugees} + \text{Refugees Joined}\)
\(\text{New Total Refugees} = 300 + 60\)
\(\text{New Total Refugees} = 360\)
Calculating How Long the Remaining Food Will Last
Now we have 9000 refugee-days of food supply remaining, and there are 360 refugees to feed. To find out how many days this remaining food will last for the new number of refugees, we divide the remaining food units by the new number of refugees:
\(\text{Days Remaining} = \frac{\text{Remaining Food Units}}{\text{New Total Refugees}}\)
\(\text{Days Remaining} = \frac{9000}{360}\)
We can simplify this fraction:
\(\text{Days Remaining} = \frac{900}{36}\)
\(\text{Days Remaining} = \frac{100}{4}\)
\(\text{Days Remaining} = 25\)
So, the rest of the food supplies would last for 25 days for the 360 refugees.
Summary of the Calculation
| Parameter | Value | Calculation/Notes |
|---|---|---|
| Initial Refugees | 300 | Given |
| Initial Duration | 45 days | Given |
| Days Passed | 15 days | Given |
| Refugees Joined | 60 | Given |
| Total Initial Food (refugee-days) | 13500 | \(300 \times 45\) |
| Food Consumed (refugee-days) | 4500 | \(300 \times 15\) |
| Remaining Food (refugee-days) | 9000 | \(13500 - 4500\) or \(300 \times (45-15)\) |
| New Total Refugees | 360 | \(300 + 60\) |
| Duration for Remaining Food | 25 days | \(9000 / 360\) |
Revision Table: Food Supply Problems
| Concept | Description | Formula Example |
|---|---|---|
| Total Work/Supply | Total capacity of the supply in terms of consumption units (e.g., refugee-days). | \(\text{Supply} = \text{Workers/People} \times \text{Days}\) |
| Work/Supply Consumed | The portion of the total supply that has been used up. | \(\text{Consumed} = \text{Initial People} \times \text{Days Passed}\) |
| Remaining Work/Supply | The portion of the supply that is left. | \(\text{Remaining} = \text{Total Supply} - \text{Consumed}\) |
| Duration with New People | How long the remaining supply lasts for a changed number of people. | \(\text{Days} = \frac{\text{Remaining Supply}}{\text{New Number of People}}\) |
Additional Information: Inverse Proportion
This problem illustrates the concept of inverse proportion. If the amount of food is fixed, the number of people and the number of days the food lasts are inversely proportional. This means if the number of people increases, the number of days the food lasts decreases proportionally, and vice versa.
In our problem, after 15 days, the remaining food was enough for 300 refugees for 30 days. When the number of refugees increased to 360, the food would last for fewer days. The relationship is:
\(300 \text{ refugees} \times 30 \text{ days} = 360 \text{ refugees} \times x \text{ days}\)
Where \(x\) is the number of days the food lasts for 360 refugees.
\(9000 = 360x\)
\(x = \frac{9000}{360}\)
\(x = 25\)
This confirms our previous calculation. Understanding inverse proportion helps in solving problems involving resources like food, work, etc., shared among a varying number of individuals over time.
Important Questions from Compound Ratios
The train fare, bus fare and air fare between 2 places are in the ratio 5 : 8 : 12, the number of passenger travelled by them is in the ratio 3 : 4 : 5 and the total fare collected on a particular day for these modes of transportation for a single trip is Rs. 1,07,000. Find the fare collected from the air passengers.
The compounded ratio of (1 ∶ 3), (6 ∶ 5) and (7 ∶10) is:
Rs. 750 are divided among A, B and C in such a manner that A : B = 5 : 2 and B : C = 7 : 13, What is B’s share?
Two numbers are in the ratio 3 : 5. If 4 is subtracted from each of these two numbers, the new numbers then are in the ratio 4 : 7. Find the smaller of the two original numbers.
A person has some coins of Rs. 10, Rs. 5, and Rs. 2 denominations. The ratio of the products of the numbers of Rs. 10 and Rs. 5 coins, the numbers of Rs. 5 and Rs. 2 coins, and the numbers of Rs. 2 and Rs. 10 coins is 3 ∶ 4 ∶ 2 respectively. What could be the minimum amount of money this person has?
