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The average height of 25 boys is $1.4m$. When 5 boys leave the group, then the average height increases by $0.15m$. What is the average height of the 5 boys who leave?A. $0.8m$B. $0.9m$C. $0.95m$D. $1.05m$

Last updated date: 13th Jul 2024
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Hint: To obtain the height of the 5 boys that left the group we will form an equation before they left and after they left of the average of the height. Firstly we will let the total height of 25 bys as $x$ and form a relation. Then we will form another equation after 5 boys left the group and simplify them to get the desired answer.

Complete step-by-step solution:
It is given to us that the average height of 25 boys is $1.4m$.
Let total height of 25 boys be $x$ so we can say that,
$\dfrac{x}{25}=1.4m$
On simplifying we get,
\begin{align} & x=1.4m\times 25 \\ &\Rightarrow x=35m \\ \end{align}…..$\left( 1 \right)$
We got the total height of 25 boys as 35
Next it is given that when 5 boys left the group the average height increased by $0.15m$.
Let new total height of 20 boys who are in the group be $y$ so we get,
\begin{align} & \dfrac{y}{20}=1.4m+0.15m \\ & \Rightarrow \dfrac{y}{20}=1.55m \\ & \Rightarrow y=20\times 1.55m \\ \end{align}
$\therefore y=31m$……$\left( 2 \right)$
So total height after 5 boys left is 31
Now we get the average height of 5 boys by subtracting equation (1) by equation (2) and dividing them by 5 as follows:
\begin{align} & \dfrac{x-y}{5} \\ & = \dfrac{35-31}{5} \\ & = \dfrac{4}{5} \\ & = 0.8m \\ \end{align}
So we got the average height of 5 boy as $0.8m$
Hence correct option is (A).

Note: Average is a single number that represents a non-empty list of numbers. It is most generally used to refer to arithmetic mean where we divide the sum of the numbers by how many numbers we are using for that average. If all the numbers are the same in a list we get their average same as the number.