A family of 8 have enough stock of rice to last for 30 days. Due to the arrival of some relatives, this food was consumed in 20 days. How many guests joined the family ?
8 * 30 = (8 + g) * 20
To find out the number of guests who joined the family, we need to calculate the rate at which the rice was consumed.
First, let's calculate the rate at which the family consumes rice:
The family has enough stock of rice to last for 30 days, and it was consumed in 20 days. So, the rate of consumption is the amount of rice divided by the number of days:
Rate of consumption = Amount of rice / Number of days
Rate of consumption = 1 / 30
Now, let's calculate the rate at which each person consumes rice:
Since there are 8 family members, the rate at which each person consumes rice is the rate of consumption divided by the number of family members:
Rate per person = Rate of consumption / Number of family members
Rate per person = (1 / 30) / 8
Rate per person = 1 / (30 * 8)
Rate per person = 1 / 240
Now, we can find the number of guests who joined the family by calculating how many extra people were added to consume the rice that was consumed in 20 days.
Let's assume the number of guests who joined the family is 'x'.
So, the total number of people consuming rice is 8 (original family members) + x (guests):
Total number of people consuming rice = 8 + x
Now, let's calculate the rate at which the rice was consumed with the additional guests:
Rate per person with guests = 1 / (30 - x)
Since the amount of rice consumed in 20 days is the same as the amount of rice that would have been consumed with the original family members and the additional guests, we can set up an equation:
Rate per person = Rate per person with guests
1 / 240 = 1 / (30 - x)
To find the value of 'x', we can cross-multiply and solve the equation:
240 = 30 - x
Simplifying the equation:
x = 30 - 240
x = -210
Since the number of guests cannot be negative, we can conclude that no guests joined the family.