Question

1/8 part of a pencil is black, 1/2 part of a remaining is white. if the remaining part is blue and the lenght of this blue part is 3 1/2 cm find the lenght of the pencil

Answer 1

Find the remaining part that is not black:

black = 1/8

Remaining parts = 1 - 1/8 = 7/8

Find the remaining part that is not white:

White = 1/2 x 7/8 = 7/16

Remaining part = 7/8 - 7/16 = 7/16

Find the total length of the pencil:

Fraction that is blue = 7/16

Length that is blue = 3 1/2 cm

Therefore,

7/16 of the pencil = 3 1/2

7/16 of the pencil = 7/2

1/16 of the pencil = 7/2 ÷ 7 = 1/2 cm

16/16 of the pencil = 1/2 x 16 = 8 cm

Answer: The length of the pencil is 8 cm

Answer 2

${\boxed {\orange {\bigstar{answer}}}}$

$\small \purple{let \: assume \: length \: of \: the \: pencil \: is \: x}$

$\small \red{as \: per \: que. \: portion(length) \: of \: black \: in \: pencil} = \frac{x}{8}$

$remaining \: portion = x - \frac{x}{8} = \frac{7x}{8}$

$so \: white \: portion = \frac{1}{2} \times \frac{7x}{8} = \frac{7x}{16}$

$so \: remaining \: portion = \frac{7x}{8} - \frac{7x}{16} = \frac{7x}{16}$

$\green{as \: per \: question}$

$\frac{7x}{10} = 3.5$

${\fcolorbox{pink}{white}{x = 8cm}}$

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