Question

In a certain shop which stocks four types of caps, there are $\dfrac{1}{3}$ as many red caps as blue and $\dfrac{1}{2}$ as many green caps as red caps. There is an equal number of green caps and yellow caps. If there are 42 blue caps, then what percent of the total caps in the shop are blue?
A) $70\% $
B) $28\% $
C) $60\% $
D) $14\% $

Answer 1

Hint: In this question, we have to find the percentage of blue caps. For this, we have to find the total caps in the shop and then by applying formula we can calculate the percentage increase.

Complete step by step solution: First of all, let us see what is given to us. We have given that there are 42 blue caps
$ \Rightarrow \text{Blue Caps} = 42$

Secondly, there are $\dfrac{1}{3}$ as many red caps as blue caps
$\begin{gathered}
   \Rightarrow \text{Red Caps} = \dfrac{1}{3}\text{Blue Caps} \\
   \Rightarrow \text{Red Caps} = \dfrac{1}{3} \times 42 = 14 \\
\end{gathered} $

We have given, that there are $\dfrac{1}{2}$ as many Green caps as red caps.
$\begin{gathered}
   \Rightarrow \text{Green Caps} = \dfrac{1}{2} \text{Red Caps} \\
   \Rightarrow \text{Green Caps} = \dfrac{1}{2} \times 14 = 7 \\
\end{gathered} $

Finally, we have given that green caps is equal to yellow caps
$\begin{gathered}
   \Rightarrow \text{Green Caps} = \text{Yellow Caps} \\
   \Rightarrow \text{Yellow Caps} = 7 \\
\end{gathered} $

We can calculate the total number of caps that is given by
$\begin{gathered}
   \Rightarrow \text{Total Caps} = \text{Blue Caps} + \text{Red Caps} + \text{Green Caps} + \text{Yellow Caps} \\
   \Rightarrow \text{Total Caps} = 42 + 14 + 7 + 7 = 70 \\
\end{gathered} $

The formula for percentage is given by
$\begin{gathered}
   \Rightarrow \text{Percentage of Blue Caps} = \dfrac{\text{Blue Caps}}{\text{Total Caps}} \times 100\% \\
   \Rightarrow \text{Percentage of Blue Caps} = \dfrac{{42}}{{70}} \times 100\% = 60\% \\
\end{gathered} $

So, the correct option is C.

Note: We can also solve it with short method. As there are 42 blue caps. So, there are 14 red caps as red caps are one-third of blue caps. We will find the number of green caps is 7 as green caps are half of the blue caps and the number of yellow caps is equal to that of green caps and hence the total number of caps is 70. 42 comes at 6 when we look at table 7. Therefore, 42, when divided by 70, gives 0.6 and hence there is $60\% $ of blue caps.