Answer
Verified
386k+ views
Hint- Here, we will be proceeding by making an equation in one variable by using the formula i.e., Amount divided among each person = $\dfrac{{{\text{Total amount to be divided}}}}{{{\text{Total number of persons}}}}$ and then solving for the unknown.
Let the original number of persons be x among which Rs 9000 is to be divided.
For the amount that each person will be getting, we will divide the total amount Rs 9000 by the original number of persons among which Rs 9000 is to be divided.
i.e., Amount that each person will be getting = Rs $\dfrac{{9000}}{x}$.
Now, when the total number of persons among which Rs 9000 is to be divided are 20 persons more than the original number of persons (x).
i.e., Number of persons amount which Rs 9000 is to be divided = (x+20) persons
Hence, amount that each person will be getting = Rs $\dfrac{{9000}}{{x + 20}}$
According to problem statement, $\dfrac{{9000}}{x} - \dfrac{{9000}}{{x + 20}} = 160$
Now, we will solve the above equation by taking x(x+20) as LCM to get the value of x.
$
\Rightarrow \dfrac{{9000}}{x} - \dfrac{{9000}}{{x + 20}} = 160
$
$
\Rightarrow \dfrac{{9000\left( {x + 20} \right) - 9000x}}{{x\left( {x + 20} \right)}} = 160
$
$
\Rightarrow \dfrac{{9000x + 180000 - 9000x}}{{x\left( {x + 20} \right)}} = 160 \\
$
$
\Rightarrow \dfrac{{180000}}{{x\left( {x + 20} \right)}} = 160 \\
$
By applying cross multiplication in the above equation, we get
$
\Rightarrow 180000 = 160x\left( {x + 20} \right)
$
$
\Rightarrow 1125 = x\left( {x + 20} \right)
$
$
\Rightarrow 1125 = {x^2} + 20x
$
$
\Rightarrow {x^2} + 20x - 1125 = 0 \\
$
$
\Rightarrow {x^2} + 45x - 25x - 1125 = 0
$
$
\Rightarrow x\left( {x + 45} \right) - 25\left( {x + 45} \right) = 0 \\
$
$
\Rightarrow \left( {x + 45} \right)\left( {x - 25} \right) = 0 \\
$
Either $\left( {x + 45} \right) = 0 \Rightarrow x = - 45$ or $\left( {x - 25} \right) = 0 \Rightarrow x = 25$
As we know that here x is representing the original number of persons among which Rs 9000 is getting divided and the number of persons will always be positive so, only positive values of x should be considered.
i.e., $x = - 45$ is neglected.
So, $x = 25$ is the correct value.
Therefore, the original number of persons among will Rs 9000 is to be divided are 25 persons.
Note- In this particular problem, we can easily see that if the number of persons (among which Rs 9000 is divided) is increased, then the amount that each person will get will automatically decrease because both of these are inversely proportional to each other.
Let the original number of persons be x among which Rs 9000 is to be divided.
For the amount that each person will be getting, we will divide the total amount Rs 9000 by the original number of persons among which Rs 9000 is to be divided.
i.e., Amount that each person will be getting = Rs $\dfrac{{9000}}{x}$.
Now, when the total number of persons among which Rs 9000 is to be divided are 20 persons more than the original number of persons (x).
i.e., Number of persons amount which Rs 9000 is to be divided = (x+20) persons
Hence, amount that each person will be getting = Rs $\dfrac{{9000}}{{x + 20}}$
According to problem statement, $\dfrac{{9000}}{x} - \dfrac{{9000}}{{x + 20}} = 160$
Now, we will solve the above equation by taking x(x+20) as LCM to get the value of x.
$
\Rightarrow \dfrac{{9000}}{x} - \dfrac{{9000}}{{x + 20}} = 160
$
$
\Rightarrow \dfrac{{9000\left( {x + 20} \right) - 9000x}}{{x\left( {x + 20} \right)}} = 160
$
$
\Rightarrow \dfrac{{9000x + 180000 - 9000x}}{{x\left( {x + 20} \right)}} = 160 \\
$
$
\Rightarrow \dfrac{{180000}}{{x\left( {x + 20} \right)}} = 160 \\
$
By applying cross multiplication in the above equation, we get
$
\Rightarrow 180000 = 160x\left( {x + 20} \right)
$
$
\Rightarrow 1125 = x\left( {x + 20} \right)
$
$
\Rightarrow 1125 = {x^2} + 20x
$
$
\Rightarrow {x^2} + 20x - 1125 = 0 \\
$
$
\Rightarrow {x^2} + 45x - 25x - 1125 = 0
$
$
\Rightarrow x\left( {x + 45} \right) - 25\left( {x + 45} \right) = 0 \\
$
$
\Rightarrow \left( {x + 45} \right)\left( {x - 25} \right) = 0 \\
$
Either $\left( {x + 45} \right) = 0 \Rightarrow x = - 45$ or $\left( {x - 25} \right) = 0 \Rightarrow x = 25$
As we know that here x is representing the original number of persons among which Rs 9000 is getting divided and the number of persons will always be positive so, only positive values of x should be considered.
i.e., $x = - 45$ is neglected.
So, $x = 25$ is the correct value.
Therefore, the original number of persons among will Rs 9000 is to be divided are 25 persons.
Note- In this particular problem, we can easily see that if the number of persons (among which Rs 9000 is divided) is increased, then the amount that each person will get will automatically decrease because both of these are inversely proportional to each other.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE