Question

(i) If \[400\dfrac{2}{5}\]kg of wheat was distributed amongst 5 men, how much did each person get?
(ii) A chord of length \[71\dfrac{1}{2}\]m has been cut into 26 pieces of equal length. What is the length of each piece?

Answer 1

Hint: In both parts of the question, first convert the given mixed fraction into improper fraction by using the relation: - \[a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}\]. Then use a unitary method to find the mass of wheat each person will get in (i) and the length of each piece in (ii).

Complete step by step answer:
Let us consider part (i) of the question.
Total weight of wheat = \[400\dfrac{2}{5}\]kg
Converting this weight from mixed fraction to the improper fraction, we have,
\[\begin{align}
  & \Rightarrow 400\dfrac{2}{5}=\dfrac{\left( 400\times 5 \right)+2}{5} \\
 & \Rightarrow 400\dfrac{2}{5}=\dfrac{2002}{5} \\
\end{align}\]
\[\Rightarrow \] Total weight of wheat = \[\dfrac{2002}{5}\]kg
Now, it is given that this weight of wheat is distributed amongst 5 men.
\[\Rightarrow \] Amount of wheat 5 men will get =\[\dfrac{2002}{5}\]kg
 \[\Rightarrow \] Amount of wheat 1 man will get = \[\dfrac{2002}{5}\times \dfrac{1}{5}\] = \[\dfrac{2002}{25}\]kg
Converting \[\dfrac{2002}{25}\] into mixed fraction, we get,
\[\Rightarrow \dfrac{2002}{25}=\dfrac{\left( 25\times 80 \right)+2}{25}=80\dfrac{2}{25}\]
\[\Rightarrow \] Each person will get \[80\dfrac{2}{25}\]kg wheat.
Now, considering part (ii) of the question,
Total length of the chord = \[71\dfrac{1}{2}\]m
Converting this length from mixed fraction to the improper fraction, we have,
\[\begin{align}
  & \Rightarrow 71\dfrac{1}{2}=\dfrac{\left( 71\times 2 \right)+1}{2} \\
 & \Rightarrow 71\dfrac{1}{2}=\dfrac{143}{2} \\
\end{align}\]
\[\Rightarrow \] Total length of the chord = \[\dfrac{143}{2}\]m
Now, it is given that the chord is cut into 26 pieces of equal length.
\[\Rightarrow \] Length of 26 pieces = \[\dfrac{143}{2}\]m
\[\Rightarrow \] Length of 1 piece = \[\dfrac{143}{2}\times \dfrac{1}{26}\]m = \[\dfrac{143}{52}\]m
Converting \[\dfrac{143}{52}\] into mixed fraction, we get,
\[\Rightarrow \dfrac{143}{52}=\dfrac{\left( 52\times 2 \right)+39}{52}=2\dfrac{39}{52}\]
\[\Rightarrow \] Length of each piece of chord = \[2\dfrac{39}{52}\]m

Note: Here, you may note that it will be difficult for us to solve the problem if we do not convert the given mixed fractions into improper fraction. Further, we have applied the basic approach of unitary method to find the length of one piece of chord or to find the amount of wheat one person will get.