# The ratio of present ages of Veena and Kinjal is 2:3. The ratio of the ages of Veena after 4 years and the age of Kinjal 4 years before is 4:1. Find their present ages.

Answer

Verified

363.3k+ views

Hint: Assume Veena’s present age to be x and Kinjal’s present age to be y. Make two equations on x and y based on the information given in the question. Solve those two equations to find the values of x and y. The values of x and y will be the required present ages.

Complete step-by-step answer:

Let us assume that Veena’s present age is x years, and Kinjal’s present age is y years.

Based on the first condition, the ratio of these two ages is 2:3.

Thus, $\dfrac{x}{y}=\dfrac{2}{3}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots \left( 1 \right)$

For the second condition, we know that since Veena’s present age is x, her age after 4 years will be $x+4$ years. Similarly, since Kinjal’s present age is y, age 4 years before would have been $y-4$years.

The ratio of these two ages is 4:1.

Hence, $\dfrac{x+4}{y-4}=\dfrac{4}{1}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots \left( 2 \right)$

From (1), we obtain$x=\dfrac{2}{3}y$. Substituting this in equation (2), we get

$\begin{align}

& x+4=4\left( y-4 \right) \\

& \Rightarrow \dfrac{2}{3}y+4=4y-16 \\

& \Rightarrow \dfrac{2}{3}y=4y-20 \\

& \Rightarrow 4y-\dfrac{2}{3}y=20 \\

& \Rightarrow \dfrac{12y-2y}{3}=20 \\

& \Rightarrow \dfrac{10y}{3}=20 \\

\end{align}$

$\begin{align}

& \Rightarrow y=\dfrac{20\times 3}{10} \\

& \Rightarrow y=6 \\

\end{align}$

Thus, the present age of Kinjal is 6 years.

Now, to find the value of x, which gives the present age of Veena, we will substitute this value of y back in the expression obtained from (1), which is $x=\dfrac{2}{3}y$.

Thus $x=\dfrac{2}{3}\times 6$

$\Rightarrow x=4$

Thus the present age of Veena is 4 years.

Note: The solution obtained, the present ages of Veena and Kinjal can be verified by checking if these values satisfy the given conditions.

For the first condition, the ratio of their present ages is $x:y=4:6=2:3$. Thus the first condition is satisfied.

For the second condition, the ratio of Veena’s age after 4 years and Kinjal’s age 4 years before, $\left( x+4 \right):\left( y-4 \right)=8:2=4:1$. Hence, the second condition is also satisfied.

Thus, we have verified that the values of x and y obtained, 4 and 6 respectively is the correct answer.

Complete step-by-step answer:

Let us assume that Veena’s present age is x years, and Kinjal’s present age is y years.

Based on the first condition, the ratio of these two ages is 2:3.

Thus, $\dfrac{x}{y}=\dfrac{2}{3}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots \left( 1 \right)$

For the second condition, we know that since Veena’s present age is x, her age after 4 years will be $x+4$ years. Similarly, since Kinjal’s present age is y, age 4 years before would have been $y-4$years.

The ratio of these two ages is 4:1.

Hence, $\dfrac{x+4}{y-4}=\dfrac{4}{1}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots \left( 2 \right)$

From (1), we obtain$x=\dfrac{2}{3}y$. Substituting this in equation (2), we get

$\begin{align}

& x+4=4\left( y-4 \right) \\

& \Rightarrow \dfrac{2}{3}y+4=4y-16 \\

& \Rightarrow \dfrac{2}{3}y=4y-20 \\

& \Rightarrow 4y-\dfrac{2}{3}y=20 \\

& \Rightarrow \dfrac{12y-2y}{3}=20 \\

& \Rightarrow \dfrac{10y}{3}=20 \\

\end{align}$

$\begin{align}

& \Rightarrow y=\dfrac{20\times 3}{10} \\

& \Rightarrow y=6 \\

\end{align}$

Thus, the present age of Kinjal is 6 years.

Now, to find the value of x, which gives the present age of Veena, we will substitute this value of y back in the expression obtained from (1), which is $x=\dfrac{2}{3}y$.

Thus $x=\dfrac{2}{3}\times 6$

$\Rightarrow x=4$

Thus the present age of Veena is 4 years.

Note: The solution obtained, the present ages of Veena and Kinjal can be verified by checking if these values satisfy the given conditions.

For the first condition, the ratio of their present ages is $x:y=4:6=2:3$. Thus the first condition is satisfied.

For the second condition, the ratio of Veena’s age after 4 years and Kinjal’s age 4 years before, $\left( x+4 \right):\left( y-4 \right)=8:2=4:1$. Hence, the second condition is also satisfied.

Thus, we have verified that the values of x and y obtained, 4 and 6 respectively is the correct answer.

Last updated date: 30th Sep 2023

•

Total views: 363.3k

•

Views today: 9.63k

Recently Updated Pages

What do you mean by public facilities

Slogan on Noise Pollution

Paragraph on Friendship

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

What is the Full Form of ILO, UNICEF and UNESCO

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Why are resources distributed unequally over the e class 7 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Briefly mention the contribution of TH Morgan in g class 12 biology CBSE

What is the past tense of read class 10 english CBSE