Answer

Verified

420.6k+ views

**Hint:**In this question, we are given a statement about ages of Raja and his father. We are also given a statement about the ages of Raja and his father after six years. Using this information, we need to calculate the present age of Raja and his father. For this, we will first suppose Raja's father's age to be x. And then present age's statement to calculate age of Raja's father in terms of x. Then we will find the age of both after 6 years by adding 6 to both of their ages. After that, we will form an equation of their ages using the statement of ages of both of them after 6 years and hence, solve it to find the value of x.

**Complete step by step answer:**

Here, we have to find the present age of Raja and his father. So, let us suppose that, present age of Raja's father is x years.

Since, Raja's age is ${{\dfrac{1}{5}}^{th}}$ of his father's age, so Raja's age will be $\dfrac{x}{5}$ years.

Now, let us find their ages 6 years later.

After 6 years, their ages will be:

Age of Raja after six years $\Rightarrow \left( \dfrac{x}{5}+6 \right)\text{years}$.

Age of Raja's father after six years $\Rightarrow \left( x+6 \right)\text{years}$.

We are given that, after 6 years, Raja's age will be one-third his father's age. Therefore, $\left( \dfrac{x}{5}+6 \right)$ will be ${{\dfrac{1}{3}}^{rd}}$ of (x+6). Hence, the equation becomes $\Rightarrow \dfrac{x}{5}+6=\dfrac{x+6}{3}$.

Taking LCM of 5 on the left side of the equation, we get:

$\Rightarrow \dfrac{x+30}{5}=\dfrac{x+6}{3}$.

Cross multiplying we get:

\[\begin{align}

& \Rightarrow 3\left( x+30 \right)=5\left( x+6 \right) \\

& \Rightarrow 3x+90=5x+30 \\

& \Rightarrow 5x-3x=90-30 \\

& \Rightarrow 2x=60 \\

& \Rightarrow x=30 \\

\end{align}\]

Since, x was supposed to be the age of Raja's father, so the age of Raja's father is 30 years.

Now, age of Raja is ${{\dfrac{1}{5}}^{th}}$ the age of his father, so Raja's age will be $\dfrac{30}{5}=6\text{ years}$.

**Hence, age of Raja = 6 years and age of Raja's father = 30 years.**

**Note:**While solving this sum, students should not get confused with present age and age after 6 years. We can also simplify our calculations assuming Raja's age as x years which will result in Raja's father's age as 5x (${{\dfrac{1}{5}}^{th}}$ of 5x is x). After 6 years, their ages will be x+6 and 5x+6. So equation will be:

\[\begin{align}

& \Rightarrow 3\left( 5x+6 \right)=5x+6 \\

& \Rightarrow 3x+18=5x+6 \\

& \Rightarrow 2x=12 \\

& \Rightarrow x=6 \\

\end{align}\]

Hence, required ages will be 6 years and $6\times 5=30\text{ years}$.

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Which are the Top 10 Largest Countries of the World?

10 examples of evaporation in daily life with explanations

Give 10 examples for herbs , shrubs , climbers , creepers

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

Difference Between Plant Cell and Animal Cell