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$3\dfrac{1}{2}$ cm is blue then what is the total length of the pencil?

A. $6$ cm

B. $7$ cm

C. $8$ cm

D. $11$ cm

Answer
Verified

Let us assume that the total length of pencil is $x$ cm. Now it is given that one-eight of the total length of pencil is of black colour. Therefore, we can say that black part of the pencil is one-eight of $x$. That is, black part $ = \dfrac{x}{8}$ cm.

Now the total length of the pencil is $x$ cm and the length of black part is $\dfrac{x}{8}$ cm. So we can say that length of remaining part is $\left( {x - \dfrac{x}{8}} \right) = \dfrac{{8x - x}}{8} = \dfrac{{7x}}{8}$ cm.

Now it is also given that half of the remaining part is of yellow colour. That is, $\dfrac{1}{2}$ of the remaining part is of yellow colour. Therefore, we can say that length of yellow part is $\dfrac{1}{2}\left( {\dfrac{{7x}}{8}} \right) = \dfrac{{7x}}{{16}}$ cm.

Now it is also given that remaining $3\dfrac{1}{2} = \dfrac{7}{2}$ cm is of blue colour but now we have remaining part of pencil is $\dfrac{{7x}}{{16}}$ . So we can say that the length of the remaining blue part is $\dfrac{{7x}}{{16}}$ which is equal to $\dfrac{7}{2}$. That is, $\dfrac{{7x}}{{16}} = \dfrac{7}{2} \Rightarrow x = \dfrac{{16}}{2} \Rightarrow x = 8$

Therefore, the total length of pencil is $8$ cm.