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# Suman’s mother is four times as old as Suman. Twenty years later, she will be just twice as old as Suman will be then. Find the present age of Suman?

Last updated date: 11th Sep 2024
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Hint: We start solving the problem by assigning the variable for the present age of Suman and find the present age of Suman’s mother using this variable. We then find the ages of Suman and Suman’s mother after 20 years by adding 20 to the ages we just obtained using the variable. We then use the condition Suman’s mother will be just twice as old as Suman will be after twenty years and make the necessary calculations to get the present age of Suman.

According to the problem, we are given that Suman’s mother is four times as old as Suman and she will be just twice as old as Suman will be after twenty years. We need to find the preset age of Suman.
Let us assume the present age of Suman is ‘x’ years.
So, we get the present age of Suman’s mother will be $4\times x=4x$ years.
Now let us find the ages of Suman and his mother after 20 years which will be $x+20$ and $4x+20$ years.
From the problem, we have said that the age of Suman’s mother will be twice the age of Suman after 20 years.
So, we have $4x+20=2\left( x+20 \right)$.
$\Rightarrow 4x+20=2x+40$.
$\Rightarrow 4x-2x=40-20$.
$\Rightarrow 2x=20$.
$\Rightarrow x=\dfrac{20}{2}$.
$\Rightarrow x=10$ years.

∴ The present age of Suman is 10 years.

Note: We should know that the present age of Suman will not be the age after 20 years which is the most common mistake many students make. Whenever we get this type of problem, we should start solving it by assuming variables for the unknowns to avoid confusions and calculation mistakes. We can also find the present age of Suman’s mother using the present age of Suman. Similarly, we can expect problems to find the difference in ages of Suman and Suman’s mother after 30 years from the present age.