Answer

Verified

447.9k+ views

**Hint:**In this problem, first we assume that the total length of pencil is $x$ cm. Then we will use the given information. We will get the linear equation in one variable. After solving the linear equation in one variable, we will get the required length of the pencil.

**Complete step-by-step answer:**

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.

**Therefore, option C is true.**

**Note:**When solving these types of problems,make sure to calculate the remaining portion appropriately in accordance with the data given.General form of linear equation in one variable is $ax + b = 0$ where $a,b$ are integers and $x$ is variable.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths