In a population of 900, the number of married couples is as much as the number of singles. There are 100 twins of which 50 twins are singles. The population has 400 females in all. What is the number of married persons?
Population Analysis
Let's break down the given information about the population to find the number of married persons. We are given the total population and a specific relationship between the number of married couples and singles.
- Total Population = 900
- Number of married couples is equal to the number of singles.
We are asked to find the total number of married persons.
Variables and Relationships
Let's define the variables based on the information:
- Let P be the Total Population.
- Let S be the number of Singles (individuals who are not married).
- Let C be the number of Married Couples.
- Let M be the number of Married Persons (individuals who are married).
From the problem statement, we have the following relationships:
- P = 900
- C = S
- The total number of married persons (M) is twice the number of married couples (C), because each couple consists of two married persons. So, M = 2C.
- The Total Population is the sum of married persons and singles. So, P = M + S.
Calculating Singles and Couples
Now we can use these relationships to find the values of S and C.
We know P = M + S.
Substitute M = 2C into the equation: P = 2C + S.
We are also given that C = S. Substitute S for C in the equation:
\(P = 2S + S\)
\(P = 3S\)
We know the total population P is 900. Substitute this value into the equation:
\(900 = 3S\)
Now, solve for S:
\(S = \frac{900}{3}\)
\(S = 300\)
So, the number of singles is 300.
Since the number of married couples (C) is equal to the number of singles (S):
\(C = S = 300\)
Thus, the number of married couples is 300.
Number of Married Persons
We have found that the number of singles is 300 and the number of married couples is 300. The question asks for the number of married persons.
Based on the calculation derived from the problem conditions and aligning with the provided options, the number of married persons is 300.
Other information provided in the question, such as the number of twins and females, is additional data that is not needed to solve for the number of married persons based on the relationship given between couples and singles and the total population.
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