Question

A piece of string is 40 cm long. it is cut into three pieces. the longest piece is 3 times as long as the middle-sized and the shortest piece is 23 cm shorter than the longest piece. find the length of the shortest piece(in cm) ? (a) 27 (b) 5 (c) 4 (d) 9

Answer 1

Suppose, the middle-sized string has the length=x

So, the length of the longest piece of string=3x and  

The length of the shortest piece of string=3x-23

Now, adding all the pieces of string, we get:

x+3x+3x-23=40

7x=40+23

7x=63

x=9

Hence, the length of the shortest piece=3x-23=4 cm

Therefore, option (c) 4 is correct.

Answer 2

Answer:

shortest piece is (c) 4 cm

Step-by-step explanation:

consider the length of middle piece as X

longest piece is 3 times middle piece = 3 X

shortest piece =3 X - 23 cm

total length of string = longest piece + middle piece + shortest piece

40 cm= 3 X + X +3 X - 23

40 cm =7 X - 23

40 cm + 23 cm = 7 X

63 cm = 7 X

X = 63/7

X = 9 cm

middle piece = X = 9 cm

longest piece = 3 X = 3×9=27 cm

shortest piece = 3 X-23 = 27-23 = 4 cm

check

9+27+4=40

40=40

hence checked