\(\frac{1}{4}\) of a wire is in black colour and half of the remaining is in white and rest 6 cm length is blue. What is the length of the wire ?

Given:

Fraction of the wire in black = \( \frac{1}{4} \)

Half of the remaining wire is white.

Rest of the wire (blue) = 6 cm

Formula used:

Let the total length of the wire be \( x \).

Black wire length = \( \frac{x}{4} \)

Remaining wire = \( x - \frac{x}{4} = \frac{3x}{4} \)

White wire length = \( \frac{1}{2} \times \frac{3x}{4} = \frac{3x}{8} \)

Blue wire length = \( x - \left(\frac{x}{4} + \frac{3x}{8}\right) \)

Calculation:

Blue wire length = 6 cm

⇒ \( x - \left(\frac{x}{4} + \frac{3x}{8}\right) = 6 \)

⇒ \( x - \left(\frac{2x}{8} + \frac{3x}{8}\right) = 6 \)

⇒ \( x - \frac{5x}{8} = 6 \)

⇒ \( \frac{3x}{8} = 6 \)

⇒ \( x = \frac{6 \times 8}{3} \)

⇒ \( x = 16 \)

∴ The total length of the wire is 16 cm.