# The sum of present ages of the father and his son is $45$ years. $5$ years ago, the age of the father is $6$ times that of the son. What is the present age of son?

Last updated date: 29th Mar 2023

•

Total views: 308.4k

•

Views today: 4.84k

Answer

Verified

308.4k+ views

Hint: Use all the given conditions. Here first we find $5$ years ago of son and father by assuming their present age and equate it to the given condition.

Complete step-by-step answer:

Let the present age of father be = $x$ years

And the present age of son be = $y$ years

Given that sum of their present ages = $45$ years

$ \Rightarrow x + y = 45 \to (1)$

$5$ Years ago, age of the father = $x - 5$ years

$5$ Years ago, age of the son = $y - 5$ years

Given the condition is that, $5$ Years ago the age of a father is $6$ times that of his son.

So,

$

\Rightarrow (x - 5) = 6(y - 5) \\

\Rightarrow (x - 5) = 6(y - 30) \\

\Rightarrow 6y - x = - 5 + 30 \\

\Rightarrow 6y - x = 25 \to (2) \\

$

Now on adding equation $(1)$ and $(2)$ we get

$

\Rightarrow x + y + 6y - x = 45 + 25 \\

\Rightarrow 7y = 70 \\

\Rightarrow y = 10 \\

$

Here we have consider that present age of son as $y$ years

Therefore the present age of a son is $10$ years.

Note: Here we have to find the $5$ years ago age of son and father, here ago means before present age where we have to subtract the present age, 5 i.e. $(x - 5)$.

Complete step-by-step answer:

Let the present age of father be = $x$ years

And the present age of son be = $y$ years

Given that sum of their present ages = $45$ years

$ \Rightarrow x + y = 45 \to (1)$

$5$ Years ago, age of the father = $x - 5$ years

$5$ Years ago, age of the son = $y - 5$ years

Given the condition is that, $5$ Years ago the age of a father is $6$ times that of his son.

So,

$

\Rightarrow (x - 5) = 6(y - 5) \\

\Rightarrow (x - 5) = 6(y - 30) \\

\Rightarrow 6y - x = - 5 + 30 \\

\Rightarrow 6y - x = 25 \to (2) \\

$

Now on adding equation $(1)$ and $(2)$ we get

$

\Rightarrow x + y + 6y - x = 45 + 25 \\

\Rightarrow 7y = 70 \\

\Rightarrow y = 10 \\

$

Here we have consider that present age of son as $y$ years

Therefore the present age of a son is $10$ years.

Note: Here we have to find the $5$ years ago age of son and father, here ago means before present age where we have to subtract the present age, 5 i.e. $(x - 5)$.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

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

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE