Question

If a person is born every $5$ seconds and a person dies every $12$ seconds, then how many seconds does it take for the population to grow by one?

Answer 1

Hint: The LCD ( Least common divisor) of the two quantities and divide by the difference of the two quantities will give the rate according to increase in growth by one.

Complete step by step answer:
As per the problem
A person is born every 5 seconds and a person dies every $12$ seconds.
Here the LCD of $5$ and $12$ is $60$
The number of person born in $60$ seconds
\[ \Rightarrow \dfrac{{60}}{5} = 12\]
The Number of person died in 12 seconds
\[ \Rightarrow \dfrac{{60}}{{12}} = 5\]
Hence Population increase in 60 seconds is
\[ \Rightarrow 12 - 5 = 7\]
Hence time required to increase the population by one
\[\dfrac{{60}}{7}\] Seconds

Net population increase = \[8.57\] seconds net population increase.

Note: There can be an alternative approach for this question
Let us look at 60 seconds because there are a whole (not fractional) number of births \[12\] and a whole number of deaths \[5\] in \[60\] seconds. Therefore, on average, the population grows at the rate of
\[\dfrac{{12 - 5}}{{60}} = \dfrac{7}{{60}}\]
The inverse of that is \[\dfrac{{\dfrac{1}{7}}}{{60}} = \dfrac{{60}}{7}\] net population increase = \[8.57\] seconds net population increase
This is a question that requires the understanding of unitary method. If one closely observes, at every step we have found the value of the quantity if it was one in number.
The unitary method is a method in which you find the value of a unit and then the value of a required number of units. What can units and values be?
Suppose you go to the market to purchase 6 apples. The shopkeeper tells you that he is selling 10 apples for Rs 100. In this case, the apples are the units, and the cost of the apples is the value. While solving a problem using the unitary method, it is important to recognize the units and values.
For simplification, always write the things to be calculated on the right-hand side and things known on the left-hand side. In the above problem, we know the amount of the number of apples and the value of the apples is unknown. It should be noted that the concept of ratio and proportion is used for problems related to this method.