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There is enough food to last for 40 people for 10 days. If 10 more people join them, the food will last for
- a)10 days
- b)12 days
- c)8 days
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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To solve this problem, we need to understand the relationship between the number of people and the amount of food needed.
Let's assume that the amount of food needed by each person per day is constant. Therefore, if there are 40 people, the amount of food needed for 10 days is 40 x 10 = 400 units of food.
Now, let's consider what happens when 10 more people join. The total number of people becomes 40 + 10 = 50 people. We need to determine how long the food will last for these 50 people.
To find the new number of days the food will last, we can use the concept of proportions. We can set up a proportion with the number of people and the number of days the food will last:
40 people / 400 units of food = 50 people / x units of food
Cross-multiplying, we get:
40x = 400 * 50
Simplifying, we find:
40x = 20,000
Dividing both sides by 40, we find:
x = 20,000 / 40
x = 500
Therefore, the food will last for 500 units of food. Now, we need to determine how many days this amount of food will last for 50 people.
If 500 units of food last for 50 people, the number of days the food will last is:
500 units of food / 50 people = 10 units of food per person
Since each person needs 10 units of food per day, the food will last for 10 days.
Therefore, the correct answer is option C) 8 days.
Let's assume that the amount of food needed by each person per day is constant. Therefore, if there are 40 people, the amount of food needed for 10 days is 40 x 10 = 400 units of food.
Now, let's consider what happens when 10 more people join. The total number of people becomes 40 + 10 = 50 people. We need to determine how long the food will last for these 50 people.
To find the new number of days the food will last, we can use the concept of proportions. We can set up a proportion with the number of people and the number of days the food will last:
40 people / 400 units of food = 50 people / x units of food
Cross-multiplying, we get:
40x = 400 * 50
Simplifying, we find:
40x = 20,000
Dividing both sides by 40, we find:
x = 20,000 / 40
x = 500
Therefore, the food will last for 500 units of food. Now, we need to determine how many days this amount of food will last for 50 people.
If 500 units of food last for 50 people, the number of days the food will last is:
500 units of food / 50 people = 10 units of food per person
Since each person needs 10 units of food per day, the food will last for 10 days.
Therefore, the correct answer is option C) 8 days.
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