Answer
414.9k+ views
Hint: Start by assuming the present age as some variable and try to form relations as per the statement given in the question. Solve the relationships formed and find out the value of the variable assumed, ignore negative value if found as age can never be negative.
Complete step-by-step solution:
Let us take the present age of the person to be ‘x’ years and the son’s age be ‘y’ years.
Now, let us form the required relation of ages.
The age of the person 5 years from now will be=$x + 5$ years
The age of the person 5 years ago was =$x - 5$ years
The age of the son 5 years from now will be=$y + 5$ years
The age of the son 5 years ago was =$y - 5$ years
Now, according to the statement given in the question, we have
$x - 5 = 7(y - 5)$
Solving this, we get
$x - 5 = 7y - 35 \\
\Rightarrow x - 7y = - 30 \to eqn.1 $
Similarly , we have one more condition,
$x + 5 = 3(y + 5)$
Solving this, we get
$ x + 5 = 3y + 15 \\
\Rightarrow x - 3y = 10 \to eqn.2 $
Solving, eqn.1 and Eqn. 2 simultaneously, we get
$ - 4y = - 40 \\
\Rightarrow y = 10 $
On substituting the value of y in equation 1 we get,
\[x = 40\]
Therefore, the present age of the person and son is 40 years and 10 years respectively.
Note: Such similar problems can be solved by following the approach of part by part work, read a statement and then form its equation or relation and repeat the same for the next statement. Attention is required while solving such questions as they can have quadratic equations, needed to be solved by either splitting middle term or discriminant rule and any negative values are to be neglected as age can never be negative.
Complete step-by-step solution:
Let us take the present age of the person to be ‘x’ years and the son’s age be ‘y’ years.
Now, let us form the required relation of ages.
The age of the person 5 years from now will be=$x + 5$ years
The age of the person 5 years ago was =$x - 5$ years
The age of the son 5 years from now will be=$y + 5$ years
The age of the son 5 years ago was =$y - 5$ years
Now, according to the statement given in the question, we have
$x - 5 = 7(y - 5)$
Solving this, we get
$x - 5 = 7y - 35 \\
\Rightarrow x - 7y = - 30 \to eqn.1 $
Similarly , we have one more condition,
$x + 5 = 3(y + 5)$
Solving this, we get
$ x + 5 = 3y + 15 \\
\Rightarrow x - 3y = 10 \to eqn.2 $
Solving, eqn.1 and Eqn. 2 simultaneously, we get
$ - 4y = - 40 \\
\Rightarrow y = 10 $
On substituting the value of y in equation 1 we get,
\[x = 40\]
Therefore, the present age of the person and son is 40 years and 10 years respectively.
Note: Such similar problems can be solved by following the approach of part by part work, read a statement and then form its equation or relation and repeat the same for the next statement. Attention is required while solving such questions as they can have quadratic equations, needed to be solved by either splitting middle term or discriminant rule and any negative values are to be neglected as age can never be negative.
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)