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?

Blue |
Black |
Red |
Yellow |

40% |
25% |
20% |
15% |

This question was previously asked in

GATE EE 2018 Official Paper

Option 3 : 43.75

CT 1: Ratio and Proportion

2672

10 Questions
16 Marks
30 Mins

Let the total number of marbles = 100

Number of blue marbles = 40

Number of black marbles = 25

Number of red marbles = 20

Number of yellow marbles = 15

And the cost of each marble = 1 unit

The total cost of marbles as per current design = 100 units

The cost of each marble after the cost of each marble is increased by 25% = 1.25 unit

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

Let the number of marbles of each colour to reduce = n

Now, the number of blue marbles = 40 – n

Number of black marbles = 25 - n

Number of red marbles = 20 - n

Number of yellow marbles = 15 - n

The total cost remains same as previous.

⇒ [(40 – n) + (25 – n) + (20 – n) + (15 – n)] [1.25] = 100

⇒ 100 – 4n = 80

⇒ n = 5

Now, the number total marbles = 100 – 4(5) = 80

The number of blue marbles = 40 – 5 = 35

The percentage of blue marbles in the new design \(= \frac{{35}}{{80}} \times 100 = 43.75\;\%\)