Answer

Verified

375.3k+ views

**Hint:**Here, we will first assume the present age of the father and the present age of the son to be any variable. Then we will form two linear equations in two variables using the given conditions. Then we will solve both the equations to get the required value of one of the variables. Using this we will find the value of another variable and hence we will get the required present value of the father and the son.

**Complete step by step solution:**

Let the present age of the father be \[x\] and the present age of the son be \[y\].

It is given that the age of the father is three times as that of the age of the son. So we can write it as:

\[x = 3y\] ………. \[\left( 1 \right)\]

12 years later, the age of the father will become \[x + 12\] and the age of the son will become \[y + 12\].

It is also given that the age of the father will be equal to 2 times the age of the son after 12 years.

So we can write it as:-

\[x + 12 = 2\left( {y + 12} \right)\]

Using the distributive property of multiplication, we get

\[ \Rightarrow x + 12 = 2y + 24\]

Now, we will subtract 12 from both sides. Therefore, we get

\[\begin{array}{l} \Rightarrow x + 12 - 12 = 2y + 24 - 12\\ \Rightarrow x = 2y + 12\end{array}\]

Now, we will substitute the value of \[x\] from equation \[\left( 1 \right)\] in the above equation.

\[ \Rightarrow 3y = 2y + 12\]

Subtracting the term \[2y\] from both sides, we get

\[\begin{array}{l} \Rightarrow 3y - 2y = 2y - 2y + 12\\ \Rightarrow y = 12\end{array}\]

Now, we will substitute the value of \[y\] in equation \[\left( 1 \right)\]. So, we get

\[x = 3 \times 12 = 36\]

**Hence, the present age of father is equal to 36 years and the present age of the son is equal to 12 years.**

**Note:**

We need to keep in mind that if we are forming the equation after certain years then the present age of the father and the son will get added by the same number of years to avoid mistakes. Here the age after 12 years is given and not before 12 years, so we will add the number of years and not subtract it. So, we need to be careful while forming an equation. A linear equation in two variables is defined as an equation which has two distinct variables and has a highest degree of 1.

Recently Updated Pages

Which are the Top 10 Largest Countries of the World?

Differentiate between Shortterm and Longterm adapt class 1 biology CBSE

How do you find slope point slope slope intercept standard class 12 maths CBSE

How do you find B1 We know that B2B+2I3 class 12 maths CBSE

How do you integrate int dfracxsqrt x2 + 9 dx class 12 maths CBSE

How do you integrate int left dfracx2 1x + 1 right class 12 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Name 10 Living and Non living things class 9 biology CBSE

The Buddhist universities of Nalanda and Vikramshila class 7 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE