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 Calculation Steps
We are given a total population of 900. We are also told that the number of married couples is equal to the number of singles.
Let's define the terms:
- A married couple consists of two married persons.
- Singles are individuals who are not married.
Let:
- \(M\) be the number of married couples.
- \(S\) be the number of singles.
From the problem statement, we have the condition:
\(M = S\)
The total number of married persons in the population is twice the number of married couples, because each couple includes two individuals. Let \(MP\) be the number of married persons.
\(MP = 2 \times M\)
The total population is the sum of all individuals, who are either married persons or singles.
\(\text{Total Population} = MP + S\)
We are given the total population is 900:
\(900 = MP + S\)
Now we use the condition \(M = S\) and the relationship \(MP = 2 \times M\). From \(MP = 2 \times M\), we can express \(M\) as \(M = \frac{MP}{2}\). Since \(S = M\), we also have \(S = \frac{MP}{2}\).
Substitute this expression for \(S\) into the total population equation:
\(900 = MP + \frac{MP}{2}\)
To find the value of \(MP\), we need to solve this equation. Combine the terms on the right side by finding a common denominator:
\(900 = \frac{2 \times MP}{2} + \frac{MP}{2}\)
\(900 = \frac{2MP + MP}{2}\)
\(900 = \frac{3MP}{2}\)
Now, multiply both sides of the equation by 2 to isolate the term with \(MP\):
\(900 \times 2 = 3MP\)
\(1800 = 3MP\)
Finally, divide both sides by 3 to find the value of \(MP\):
\(MP = \frac{1800}{3}\)
\(MP = 600\)
Thus, the number of married persons is 600.
Essential Population Data Analysis
The problem provides additional details about the population, such as the number of twins (100 total, 50 single) and the total number of females (400). Let's consider if this information is necessary to find the number of married persons.
- The primary condition given is the relationship between married couples and singles, alongside the total population size.
- The calculation derived (\(\text{Total Population} = MP + S\) and \(S = MP/2\)) uses only the total population and the relationship between married status groups.
The details about twins and females provide specific demographic breakdowns within the population (e.g., how many singles are twins, the gender distribution) but do not alter the overall counts of married persons and singles that sum up to the total population according to the initial conditions. Therefore, this additional information is not required to solve for the number of married persons in this particular problem.
Based on the fundamental relationship between married persons and singles given the total population, the number of married persons is calculated to be 600.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
