Question

A ribbon is cut into 3 pieces in the ratio 3:2:7. If the total length of the ribbon is 24m. Find the length of each piece.

Answer 1

Hint: First of all, we will suppose the length of the three pieces of the ribbon according to the given ratio in which the ribbon is cut into 3 pieces in the ratio 3:2:7 and then, we will equate the sum of its pieces with the total length of the ribbon.

Complete step-by-step answer:
We have been given that a ribbon is cut into 3 pieces in the ratio 3:2:7 and the total length of the ribbon is 24m. So, we have to find the length of each piece.
Let us suppose, the length of 3 pieces in which a ribbon is cut are 3x, 2x and 7x, according to the given ratio.
Since, the total length of the ribbon is 24m, we can add the lengths in terms of x and then equate it to 24m. Therefore, we will get the equation as below,
\[\begin{align}
  & \Rightarrow 3x+2x+7x=24 \\
 & \Rightarrow 12x=24 \\
\end{align}\]
On dividing the equation by 12 on both sides and simplifying, we get:
\[\Rightarrow x=\dfrac{24}{2}=2\]
Now, we have got the value of x. We had assumed the lengths as 3x, 2x and 7x. Now, we can substitute the value of x in these lengths to get the actual length of cut pieces.
So, the length of each pieces are as follows:
\[\begin{align}
  & 3x=3\times 2=6m \\
 & 2x=2\times 2=4m \\
 & 7x=7\times 2=14m \\
\end{align}\]
Therefore, the lengths of each piece are 6m, 4m and 14m.

Note: We can also find the length of each piece by using the another method in which each length of the pieces are given by,
\[\begin{align}
  & \text{Length 1 = }\dfrac{{{x}_{1}}}{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}\times 24m \\
 & \text{Length 2 = }\dfrac{{{x}_{2}}}{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}\times 24m \\
 & \text{Length 3 = }\dfrac{{{x}_{3}}}{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}\times 24m \\
\end{align}\]
Where, the ratio in which the ribbon is cut into the three pieces is \[{{x}_{1}}:{{x}_{2}}:{{x}_{3}}\]