Question

Long length of rope needs to be cut in the ratio $6:2:1$ . How long is the longest piece of rope from a $54m$ length of rope?

Answer 1

Hint: To solve this we should know about what is ratio and how to get ratio.
Ratio: It is a relation between two numbers which show how much bigger one quantity is than the other one.For example, the ratio of boys to girls in this class is three to one that means the number of boys is three times than the number of girls.

Complete step by step solution:
As we know the ratio is compression between two numbers.
Here is given the compression between lengths of the piece of rope. How much is one is greater than the first piece and how much second is bigger than the first one.
So, here it is given that the third rope is $6$ times bigger than the first rope and the second rope is $2$ times bigger than the first piece.
Let, multiply them with a variable $x$ . Then the sum of all will equal to the total length of parental rope as it cuts it from them.
So, length of first piece $ = x$
Length of second piece $ = 2x$
Length of third piece $ = 6x$
As total length of the rope is $ = 54m$
So, add them and keep it equal to total length,
$x + 2x + 3x = 54m$
$ \Rightarrow 9x = 54m$
$ \Rightarrow x = \dfrac{{54m}}{9} = 6m$
So, length of longest piece is $ = 6x = 6 \times 6m = 36m$

Note: Ratio have numerous applications in various fields on a daily basis. Used in Finance-current ratio, debt-equity ratio, etc. Used in chemistry to know the ratio of quantity of chemical to be mixed in a chemical reaction. Used to solve mathematical problems involving - speed – distance – time, boat and stream problems, etc.