Answer

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**Hint:**In this problem, we are given that the mean of 5 numbers is 20, if one number is excluded their mean is 15 we have to find the excluded number. We know that the formula for mean is the sum of the numbers divided by the total number. we can first find the sum of the given total number 5 and mean value 20, we can then find the sum whose mean value is 15 and if one number is excluded we will have total number 4. We can then subtract both the sums to get the excluded number.

**Complete step by step answer:**

Here we are given that the mean of 5 numbers is 20, if one number is excluded their mean is 15 we have to find the excluded number.

We know that the formula to find the mean value is,

\[\Rightarrow \dfrac{Sum}{Total}=Mean\]

We can now substitute the given values, where the total number is 5 and the mean value is 20.

\[\begin{align}

& \Rightarrow \dfrac{Sum}{5}=20 \\

& \Rightarrow Sum=100......\left( 1 \right) \\

\end{align}\]

We can now find the sum, whose mean value is 15 and the total value is 4 (where 1 number is excluded from the total number 5), we get

\[\begin{align}

& \Rightarrow \dfrac{Sum}{4}=15 \\

& \Rightarrow Sum=60......\left( 2 \right) \\

\end{align}\]

We can now subtract (1) and (2), we get

\[\Rightarrow 100-60=40\]

The excluded number is 40.

**So, the correct answer is “Option B”.**

**Note:**We should always remember that the formula for mean is the sum of the numbers divided by the total number. We should also understand that if one number is excluded means, from the total of 5 numbers one id excluded and we will get the total as 4.

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