GATE2018 EE: GA-9

Question

A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles of each colour used in the current design. The cost of each marble increased by $25\%.$ Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep the total cost unchanged. What is the percentage of blue marbles in the new design$?$

$$\begin{array}{|l|l|l|l|} \hline \textbf{Blue} & \textbf{Black} & \textbf{Red} & \textbf{Yellow} \\\hline \text{40%} & \text{25%} & \text{20%} & \text{15%} \\\hline \end{array}$$

• A. $35.75$
• B. $40.25$
• C. $43.75$
• D. $46.25$

Answer 1

Assuming total marbles $=100$ 

& Cost of each marble $=1 \text{ Re.}$

∴ To buy $100$ marbles designer need to spend $100 \times 1 = 100 \text{ Rs.}$

After increasing price cost of $100$ marbles = $\text{125 Rs.}$

Now, at $100$ Rs. the designer can buy $\dfrac{100}{125} \times100 = \text{ 80 marbles}$

the designer decided to reduce equal numbers of marbles of each colour to keep the total cost unchanged.

Therefore $(40 - x) + (25 - x) + (20 - x) + (15 - x) = 80$

   $4x = 100 - 80$

   $ x = 5$

Percentage of blue marbles in the new design $=\dfrac{40 - 5}{80} \times 100$

$\qquad \qquad =\dfrac{35}{80} \times 100$

$\qquad \qquad =43.75$  

Hence, the answer is option C

Comments

a little more explanatory:

$125rs\rightarrow100\ Marbles$

$100rs\rightarrow\ ?$

$?=100\times \dfrac{100}{125}=80\ Marbles$

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nice approach mam!

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Intuitive approach after calculating how many marbles one can buy after increment in price:

Initially there were 100 marbles and after increment in price of marble by 25%, we can only buy 80 marbles.

This implies that 100-80 = 20 marbles are to be removed. Now we have to remove all marbles by equal amount and there are 4 different colors of marbles.

So we need to remove exactly 20/4 = 5 marbles from each color.

Answer 2

Answer should be (C)

Let ,In old design , Total Marbles = 100

So , Number of blue,black,red and yellow marbles should be 40,25,20,15 respectively.

Let cost of each marble = x . So , Total cost for 100 marbles in old design = 100x

Now, For new design , Let we reduce 't' marbles from each blue , black,red and yellow marbles of old design.

So, In new design ,number of blue , black, red and yellow marbles should be (40-t) ,  (25-t) ,(20-t) , (15-t)  respectively.

Now ,According to question , cost of each marble is increased by 25% . So , In new design , cost of each marble will be x + (25/100)*x = 5x/4. So, here , Total cost =  [(40-t) +  (25-t) + (20-t) + (15-t) ]*(5x/4) = (100 - 4t)*(5x/4)

Now , According to given condition cost of old design of marbles = cost of new design of marbles

So, 100x = (100 - 4t)*(5x/4) .After solving, we get t = 5

So , In new design , number of blue,black,red and yellow marbles will be (40-5) ,  (25-5) ,(20-5) , (15-5) ie. 35,20,15,10 respectively.

So, here , Total marbles = 80 and blue marbles = 35 . So , % of blue marbles = (35/80)*100 = 43.75