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**Hint:**We need to first find the general theorem for the value increase by percentage. We increase the value of a number by a certain percentage and use the theorem $x\left( 1+\dfrac{m}{100} \right)=y$. For our given problem we replace those values to get the required number.

**Complete step by step solution:**

We have to find the value of the number which can be achieved by increasing 200 by 20%.

Let us take two arbitrary numbers x and y where we know that we can get y by increasing the value of x by m%.

Then the relation can be expressed as $x\left( 1+\dfrac{m}{100} \right)=y$.

Similarly, we get our required number by increasing the number 200 by 20%.

We replace the values where we take $x=200,m=20$.

The new value of the number will be $200\left( 1+\dfrac{20}{100} \right)$.

We try to find the fraction value of $\dfrac{20}{100}$. 100 is divisible by 20. It’s also GCD of 20 and 100.

So, $\dfrac{20}{100}=\dfrac{1}{5}$. We place the value and get $200\left( 1+\dfrac{1}{5}

\right)=200\left( \dfrac{6}{5} \right)$

The multiplied form is $\dfrac{200\times 6}{5}=40\times 6=240$.

**Therefore, increasing Two hundred by 20%, we get 240.**

**Note:**We need to remember that the decrease of numbers or anything by percentage works in the same way. The formula for decrease is $x\left( 1-\dfrac{m}{100} \right)=y$. The sign in between is only different. We can also express the primary number with respect to the new number where \[x=\dfrac{y}{\left( 1\pm \dfrac{m}{100} \right)}\].

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