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**Hint:**Here, we have to find the value of forty percent of an unknown number. So first of all suppose the number is $x$ then calculate its three sevenths, then one third and then two fifths of the previous number and this number is equal to $15$. And after solving the equation we get the number and then find its forty percent.

**Complete step-by-step solution:**

Here, we have to calculate forty percent of a number.

Let the required number be $x$.

Three seventh of the number $x = \dfrac{3}{7}x$.

Now, one- third of the number $\dfrac{3}{7}x = \dfrac{1}{3} \times \dfrac{3}{7}x = \dfrac{1}{7}x$.

Now, two- fifth of the number $\dfrac{1}{7}x = \dfrac{2}{5} \times \dfrac{1}{7}x$.

Here, it is given that two- fifth of one- third of one- seventh of number $x$ is $15$.

So, $\dfrac{2}{{35}}x = 15$

$ \Rightarrow x = \dfrac{{15 \times 35}}{2}$

$\therefore x = \dfrac{{525}}{2}$

Thus, the required number is $\dfrac{{525}}{2}$.

Now, we have to calculate the forty percent of the number we got above.

So, forty percent of $\dfrac{{525}}{2}$.

$ = 40\% $of $\dfrac{{525}}{2}$.

$ = \dfrac{{40}}{{100}} \times \dfrac{{525}}{2}$.

$ = 105$.

Thus, forty percent of the required number is $105$.

**Hence, option (C) is the correct answer for this question.**

**Note:**The most crucial point where we have to give special care is when we are writing equations.

Suppose the number and proceed according to the given statement and finally equates it with the given numerical value.

Percent means a part in every hundred. $x\% $ means $x$ parts in a total of hundred parts. Mathematically it is written as $\dfrac{x}{{100}}$.

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