# 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 are equal numbers 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%

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Hint:Here in this question total number of blue caps given ,$\dfrac{1}{3}$ of total number of blue caps gives red caps and $\dfrac{1}{2}$ of red caps gives green caps.In question they given number of green caps is same as yellow caps. Add all the number of caps of different colors and find the percentage which is our required answer.

Formula used: The percentage, say P,is given by $P = \dfrac{{value}}{{total}} \times 100$.

Given, There are 42 blue caps.
There are $\dfrac{1}{3}$ as many red caps as blue.
$\Rightarrow \dfrac{1}{3} \times 42 = 14$
Therefore, there are 14 red caps.
And, It is given that $\dfrac{1}{2}$ as many green caps as red caps.
$\Rightarrow \dfrac{1}{2} \times 14 = 7$
Therefore, the number of green caps is 7.
As given, the number of yellow and green caps is the same.
Therefore, there are 7 yellow caps.
$\text{Total number of caps}= 42 + 14 + 7 + 7 = 70$
The total number of caps is 70.
The percentage, say P,is given by $P = \dfrac{{value}}{{total}} \times 100$.
Here, we have to find the percentage of blue caps. The number of blue caps is 42 and the total number of caps is 70.
$\Rightarrow p = \dfrac{{42}}{{70}} \times 100 = 60\%$

So, the correct answer is “Option C”.

Note: the question can also be framed asking the percentage of red color caps or any color cap.
The percentage of red color caps will be, the number of red caps is 14. The total number of the cap is 70.
$P = \dfrac{{value}}{{total}} \times 100 \\ \Rightarrow p = \dfrac{{14}}{{70}} \times 100 \\ \Rightarrow p = 20\% \\$