Answer
427.8k+ views
Hint: This is an Age based question and, in this question, we have to find the present ages of a mother and her daughter. First, we have to find a relation between the ages of the mother and the daughter then using that relation we can find the present ages of both of them.
Complete step-by-step answer:
Given:
Let us assume,
The present age of daughter Rekha is \[x\] years and the present age of mother Mrs. Goel is $y$ years.
Then according to the question,
The present age of mother Mrs. Goel = The present age of daughter Rekha + 27 years
So,
$\Rightarrow y = x + 27$
This is our first equation.
Now,
The age of mother Mrs. Goel after 8 years $ = \left( {y + 8} \right)$
And the age of daughter Rekha after 8 years $ = \left( {x + 8} \right)$
So, according to the question we have,
The age of mother Mrs. Goel after 8 years = $2 \times $( the age of daughter Rekha after 8 years)
$
\Rightarrow \left( {y + 8} \right) = 2 \times \left( {x + 8} \right)$
From first equation, substituting the value of $y$ in this equation we get,
$
\Rightarrow \left( {x + 27 + 8} \right) = 2x + 16\\
x + 35 = 2x + 16
$
Solving this we get,
$x = 19$
And substituting this value of $x$ in equation one we get,
$
y = 19 + 27\\
y = 46
$
Therefore, the present age of the daughter Rekha is 19 years and the present age of the mother Mrs. Goel is 46 years respectively.
So, the correct answer is “Option C”.
Note: The alternate method of solving this question was to find two equations in terms of their ages which means in terms of $x$ and $y$ then solve those equations and find the value of their ages.
The equations we get are as following,
The first equation
$y = x + 27$
Or,
$x - y = - 27$
And similarly, the second equation
$
\left( {y + 8} \right) = 2 \times \left( {x + 8} \right)\\
y + 8 = 2x + 16\\
2x - y = - 8
$
From second equation – first equation we get,
$
2x - y - \left( {x - y} \right) = - 8 - \left( { - 27} \right)\\
x = 19
$
And substituting this value of $x$ in the first equation we get,
$
x - y = - 27\\
19 - y = - 27\\
y = 19 + 27\\
y = 46
$
Therefore, the age of daughter $ = 19{\rm{ years}}$
Complete step-by-step answer:
Given:
Let us assume,
The present age of daughter Rekha is \[x\] years and the present age of mother Mrs. Goel is $y$ years.
Then according to the question,
The present age of mother Mrs. Goel = The present age of daughter Rekha + 27 years
So,
$\Rightarrow y = x + 27$
This is our first equation.
Now,
The age of mother Mrs. Goel after 8 years $ = \left( {y + 8} \right)$
And the age of daughter Rekha after 8 years $ = \left( {x + 8} \right)$
So, according to the question we have,
The age of mother Mrs. Goel after 8 years = $2 \times $( the age of daughter Rekha after 8 years)
$
\Rightarrow \left( {y + 8} \right) = 2 \times \left( {x + 8} \right)$
From first equation, substituting the value of $y$ in this equation we get,
$
\Rightarrow \left( {x + 27 + 8} \right) = 2x + 16\\
x + 35 = 2x + 16
$
Solving this we get,
$x = 19$
And substituting this value of $x$ in equation one we get,
$
y = 19 + 27\\
y = 46
$
Therefore, the present age of the daughter Rekha is 19 years and the present age of the mother Mrs. Goel is 46 years respectively.
So, the correct answer is “Option C”.
Note: The alternate method of solving this question was to find two equations in terms of their ages which means in terms of $x$ and $y$ then solve those equations and find the value of their ages.
The equations we get are as following,
The first equation
$y = x + 27$
Or,
$x - y = - 27$
And similarly, the second equation
$
\left( {y + 8} \right) = 2 \times \left( {x + 8} \right)\\
y + 8 = 2x + 16\\
2x - y = - 8
$
From second equation – first equation we get,
$
2x - y - \left( {x - y} \right) = - 8 - \left( { - 27} \right)\\
x = 19
$
And substituting this value of $x$ in the first equation we get,
$
x - y = - 27\\
19 - y = - 27\\
y = 19 + 27\\
y = 46
$
Therefore, the age of daughter $ = 19{\rm{ years}}$
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science 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)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 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)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![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)
How do you graph the function fx 4x class 9 maths 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)