Question

In a bundle of 20 sticks, there are 4 sticks each of length 1 m 50cm, 10 sticks each of length 2 m, and each of the rest of length 1 m. what is the average length of the sticks in the bundle?
a) \[{\rm{1}}{\rm{.2 m}}\]
b) \[{\rm{1}}{\rm{.5 m}}\]
c) \[{\rm{1}}{\rm{.6 m}}\]
d) \[{\rm{1}}{\rm{.8 m}}\]

Answer 1

Hint: In this question we have to find the value of the average length of the sticks in the bundle. For that, we are going to solve using the average formula. To use the average formula we will initially find the length of the given number of sticks by multiplying it with the length and summing them and then divide the sum with the total number of sticks. This is explained in a complete step by step solution.

Formulas used:
\[{\text{Average number = }}\dfrac{{{\text{Sum of observations}}}}{{{\text{Total number of observations}}}}\]

Complete step by step answer:
It is given that total number of sticks = \[20\]
Here also it is given that there are \[4\] sticks each of length \[{\rm{1 m 50}}\;{\rm{cm}}\].
That is the length of four sticks is given by \[4 \times 1.5\]
Also, it is given that there are \[10\] sticks each of length \[{\rm{2 m}}\].
That is the length of ten sticks is \[10 \times 2\].
We should find the remaining number of sticks since it is given that the remaining sticks are of length \[{\rm{1 m}}\].
\[{\text{Remaining number of sticks = total number of sticks - the number of sticks we have}}\]
\[{\text{Remaining sticks = 20 - (10 + 4) = 6}}\]
Also we have there are 6 sticks each of length \[{\rm{1 m}}\]
That is the length of six sticks \[6 \times 1\].
As we know that \[{\text{average length = }}\dfrac{{{\text{sum of all lengths}}}}{{{\text{total number of sticks}}}}\]
\[{\text{Average length}} = \dfrac{{4 \times 1.5 + 10 \times 2 + 6 \times 1}}{{20}}\]
Let us now multiply the terms in the numerator we get,
\[ \Rightarrow \dfrac{{6 + 20 + 6}}{{20}}\]
Now by adding the terms in the numerator we get the following fraction,
\[ \Rightarrow \dfrac{{32}}{{20}}\]
By dividing the elements in the numerator and denominator we get,
\[{\text{Average length = 1}}{\rm{.6}}\]

$\therefore$ The average length of the given 20 sticks is \[1.6m\].

Note:
Here we can initially multiply the length of the sticks and then add it, that is we can multiply \[4 \times 1.5\], \[10 \times 2\], and \[6 \times 1\] then add them together in the numerator. Also, we should be careful in finding the remaining number of sticks which are of length \[{\rm{1 m}}\].