Question

A piece of string is 80cm long. It is cut into three pieces. The longest piece is 3times as long as the middle-sized piece and the shortest piece is 46cm shorter than the longest piece. Find the length of the shorter piece.
(a) 14cm
(b) 10cm
(c) 8cm
(d) 18cm

Answer 1

Hint: We will assume that length of middle size piece is let say ‘x cm’ then that of longest pieces will be 3 times of middle piece so, we get as ‘3x cm’ and shortest pieces is 46cm shorter than longest piece so, we get as ’ $3x-46$ cm’. Then on adding all this value we will equate it with the total length of string i.e. 80cm. Thus, on solving we will get the value of x and putting that value in the equation of shortest piece we will get an answer.

Complete step-by-step answer:
Here, we are given the total length of string is 80cm. Now, it is cut into three pieces.
We will assume that the size of the middle piece will be ‘x’. It is given that the longest piece is 3times as long as the middle-sized piece. So, we can write it as the longest piece as ‘3x’. Also, the shortest piece is 46cm shorter than the longest piece. So, we can write it as shortest piece is $3x-46$ . thus, we can write as
Middle piece $=x$
Longest piece $=3x$
Shortest piece $=3x-46$
Now, the total length of this string is 80cm. So, on adding all the pieces which is equal to 80cm we get it as
$x+3x+3x-46=80$
On further solving, we get as
$7x-46=80$
Now, we will keep x term on left hand side and constant term on right hand side and solving we get it as
$7x=80+46=126$
We will divide both side by 7, so we get value of x term as
$x=\dfrac{126}{7}=18cm$
Thus, we get a length of middle size piece i.e. x as 18cm.
Now, we are asked to find the length of the shortest piece i.e. $=3x-46$ . So, on putting value of x we will get length as
$=3\left( 18 \right)-46=54-46$
$=8cm$
Hence, option (c) is the correct answer.


Note: Generally, mistakes happen while assuming the length of pieces. If students’ mis-interpret the sentence i.e. the longest piece is 3 times as long as the middle-sized piece, then they will assume the longest piece as x cm and that of middle piece to be 3x cm. Then the length of the shortest piece is $x-46$ cm.
Thus, on solving we will get a value of x as $x+3x+x-46=80$ . On further solving, we get $5x=126$ . Thus, the value of x will be in decimal value which is wrong. So, please be careful while assuming the variable in order to avoid mistakes.