Question

1/4 of a wire is in black colour and half of the remaining is in white and rest 6 cm length is blue. what is tje length of the wire?

Answer 1

$let \: the \: length \: of \: the \: wire \: = \: x \: cm$

$portion \: of \: black \: colour =\dfrac{x}{4}$

$portion \: of \: white \: color = \dfrac{1}{2} ( \dfrac{3x}{4}) = \dfrac{3x}{8}$

$portion \: of \: the \: blue \: colour = 6cm$

According to the given question -

$x - (\dfrac{x}{4} + \dfrac{3x}{8} )$

$x - ( \dfrac{2x + 3x}{8} )$

$x - \dfrac{5x}{8}$

$\dfrac{8x - 5x}{8} = \dfrac{3x}{8}$

$given \: portion \: of \: blue \: color \: is \: 6cm$

$\dfrac{3x}{8} = 6$

$3x = 48$

$x = \dfrac{48}{3} = 16$

$x = 16$

$\bold{Total \: length \: of \: the \: wire \: is \: 16 \: cm }$

Answer 2

Define x:

Let x be the length of the wire.

Find the length of the wire that is black:

Black = 1/4 x (Given)

Find the remaining length:

Remaining = 1 - 1/4 x = 3/4 x

Find the length that is white:

White = 1/2 of the remaining

White = 1/2 x 3/4 x = 3/8 x

Find the remaining length:

Remaining length = 3/4 x - 3/8 x = 3/8 x

Solve x:

Blue = remaining = 3/8x

Blue = 6 cm

3/8 x = 6

1/8 x = 6 ÷ 3 = 2 cm

8/8 x = 2 x 8 = 16 cm

Answer: The original length is 16 cm