Answer
352.5k+ views
Hint: We will consider Salil’s age be $x$ years and Sargams’s age $y$ years. Then from the given data we will form two equations and then we will solve them to get the value of $x$ and $y$. These will be the ages or we can say present ages of Salil and Sargam.
Complete step by step solution:
Let the present ages of Salil and Sargam be x and y years respectively.
The first condition is, Salil’s age is $23$ years more than half of Sargams’s age. This can be formed in the equation as,
\[x = \dfrac{y}{2} + 23\] ….equation (1)
taking the LCM on RHS,
\[x = \dfrac{{y + 23 \times 2}}{2}\]
On cross multiplying $2$ and taking the product on RHS,
\[2x = y + 46\]
Taking the variables on one side we get,
\[2x - y = 46\] this is simplified equation (1)
Now from the second condition, five years ago, the sum of their ages was $55$ years. This can be formed in the equation as,
\[\left( {x - 5} \right) + \left( {y - 5} \right) = 55\] …..equation (2)
On solving the brackets,
\[x + y - 10 = 55\]
Taking the constants on one side we get,
\[x + y = 55 + 10\]
\[\Rightarrow x + y = 65\] this is simplified equation (2)
On adding equation1 and equation (2),
\[2x - y + x + y = 46 + 65\]
Cancelling y and adding the x terms from the equation we get,
\[3x = 111\]
Now on dividing 111 by 3 we get,
\[x = \dfrac{{111}}{3}\]
\[ \Rightarrow x = 37\]
Now this is the present age of Salil. Now putting this value in any of the simplified equations we get,
\[ y = 65 - x \\
\Rightarrow y = 65 - 37 \\
\Rightarrow y = 28 \\
\]
This is the present age of Sargam.
Therefore, the present ages of Salil and Sargam are 37 years and 28 years respectively.
Note:
Note that forming the equation using the data or condition is the most important part of these problems. Because solution of the equation is the answer of the question.
Also note that some years before is subtracting this number from the present age and some years from now means adding that number in the present age.
Complete step by step solution:
Let the present ages of Salil and Sargam be x and y years respectively.
The first condition is, Salil’s age is $23$ years more than half of Sargams’s age. This can be formed in the equation as,
\[x = \dfrac{y}{2} + 23\] ….equation (1)
taking the LCM on RHS,
\[x = \dfrac{{y + 23 \times 2}}{2}\]
On cross multiplying $2$ and taking the product on RHS,
\[2x = y + 46\]
Taking the variables on one side we get,
\[2x - y = 46\] this is simplified equation (1)
Now from the second condition, five years ago, the sum of their ages was $55$ years. This can be formed in the equation as,
\[\left( {x - 5} \right) + \left( {y - 5} \right) = 55\] …..equation (2)
On solving the brackets,
\[x + y - 10 = 55\]
Taking the constants on one side we get,
\[x + y = 55 + 10\]
\[\Rightarrow x + y = 65\] this is simplified equation (2)
On adding equation1 and equation (2),
\[2x - y + x + y = 46 + 65\]
Cancelling y and adding the x terms from the equation we get,
\[3x = 111\]
Now on dividing 111 by 3 we get,
\[x = \dfrac{{111}}{3}\]
\[ \Rightarrow x = 37\]
Now this is the present age of Salil. Now putting this value in any of the simplified equations we get,
\[ y = 65 - x \\
\Rightarrow y = 65 - 37 \\
\Rightarrow y = 28 \\
\]
This is the present age of Sargam.
Therefore, the present ages of Salil and Sargam are 37 years and 28 years respectively.
Note:
Note that forming the equation using the data or condition is the most important part of these problems. Because solution of the equation is the answer of the question.
Also note that some years before is subtracting this number from the present age and some years from now means adding that number in the present age.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![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)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english 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)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)