Answer
369.7k+ views
Hint: To solve this question first of all assume two variables x and y as the number of cows and number of hens respectively. We know that both cow and hen have 1 head, the cow has 4 feet and the hen has 2 feet. Now using the given two conditions makes a linear equation of two variables and solves them finally to get the value of x and y.
Complete step-by-step solution:
This question is a type of linear equation in two variables, we will first make a linear equation and then solve them to get the required result.
Let the number of cows is x and the number of hens is y.
Given the total number of heads = 48.
Since each cow and hen have one head,
\[\Rightarrow x+y=48\] - (1)
Given that number of feet = 140.
Now a cow has 4 feet and a hen has 2 feet.
\[\Rightarrow \] Number of feets of all cows = 4x.
And the number of feets of all hens = 2y.
Now the total number of feet = number of feets of cow + number of feets of hens.
\[\Rightarrow \] Number of feet = 140
\[\Rightarrow 4x+2y=140\] - (2)
Now we will solve the two-equations (1) and equation (2).
Multiplying equation (1) by 2 and subtracting we get;
\[4x+2y=140\]
\[\underline{\begin{align}
& 2x+2y=96 \\
& -- \\
\end{align}}\]
\[2x=44\]
\[\Rightarrow x=\dfrac{44}{2}=22\]
Then the number of cows = x = 22.
Now we have from equation (1) we have,
\[x+y=48\]
\[\Rightarrow y=48-x\]
Substituting value of x = 22.
\[\begin{align}
& \Rightarrow y=48-22 \\
& \Rightarrow y=26 \\
\end{align}\]
Then the number of hens = y = 26. .
Note: The student can get confused by assuming both the variables are the same. Do not assume the same variable, the number of hens and the number of cows may differ so assume different variables. Also, be cautious while calculating the number of feet, the number of feet of a cow and of a hen is not the same. To avoid mistakes at this point.
Complete step-by-step solution:
This question is a type of linear equation in two variables, we will first make a linear equation and then solve them to get the required result.
Let the number of cows is x and the number of hens is y.
Given the total number of heads = 48.
Since each cow and hen have one head,
\[\Rightarrow x+y=48\] - (1)
Given that number of feet = 140.
Now a cow has 4 feet and a hen has 2 feet.
\[\Rightarrow \] Number of feets of all cows = 4x.
And the number of feets of all hens = 2y.
Now the total number of feet = number of feets of cow + number of feets of hens.
\[\Rightarrow \] Number of feet = 140
\[\Rightarrow 4x+2y=140\] - (2)
Now we will solve the two-equations (1) and equation (2).
Multiplying equation (1) by 2 and subtracting we get;
\[4x+2y=140\]
\[\underline{\begin{align}
& 2x+2y=96 \\
& -- \\
\end{align}}\]
\[2x=44\]
\[\Rightarrow x=\dfrac{44}{2}=22\]
Then the number of cows = x = 22.
Now we have from equation (1) we have,
\[x+y=48\]
\[\Rightarrow y=48-x\]
Substituting value of x = 22.
\[\begin{align}
& \Rightarrow y=48-22 \\
& \Rightarrow y=26 \\
\end{align}\]
Then the number of hens = y = 26. .
Note: The student can get confused by assuming both the variables are the same. Do not assume the same variable, the number of hens and the number of cows may differ so assume different variables. Also, be cautious while calculating the number of feet, the number of feet of a cow and of a hen is not the same. To avoid mistakes at this point.
Recently Updated Pages
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of friction in our daily life
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The amazon rainforest are called A Heart of the planet class 12 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Who was the Congress President at the time when India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)