GATE 2018 EE GA Q.9: solution and answer

GATE 2018 · EEGA Q.9 · 2 marks · MCQ

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% |

GATE 2018 EE GA question 9: A one-row data table with four columns headed Blue, Black, Red, Yellow; — Figure from the GATE 2018 EE paper. It is part of the question.

(A)
35.75
(B)
40.25
(C)
43.75
(D)
46.25

Answer and solution

ANSWER

Official answer: CSource: Official answer key, GATE 2018 EE (IIT Guwahati)

Take $100$ marbles in the current design, each costing $c$ . Any total works because the answer is a ratio; $100$ just makes the percentages whole numbers. The table gives Blue $40$ , Black $25$ , Red $20$ , Yellow $15$ marbles, so the total cost is $100 c$ .
The new price per marble is $1.25 c$ . To keep the total cost the same, the new number of marbles $n$ must satisfy $n \times 1.25 c = 100 c$ , which gives $n = \frac{100}{1.25} = 80$ .
So $100 - 80 = 20$ marbles are removed. They are removed in equal numbers from the four colours, so $\frac{20}{4} = 5$ marbles of each colour go.
Blue marbles left: $40 - 5 = 35$ .
The percentage is taken over the new total, not the old one: $\frac{35}{80} \times 100 = 43.75%$
Check: the other colours become $25 - 5 = 20$ , $20 - 5 = 15$ and $15 - 5 = 10$ , and $35 + 20 + 15 + 10 = 80$ , as required. The answer is (C) 43.75.

KEY IDEA

A fixed budget with a 25% higher price per marble buys $\frac{1}{1.25} = 0.8$ times as many marbles, so 20% of the marbles go. Because they are removed in equal numbers from each of the four colours, each colour loses 5% of the original total. That leaves blue at $40 - 5 = 35$ out of $80$ .

WATCH OUT FOR

Removing the same percentage from every colour. That leaves blue at 40%, which is not an option. The question says equal numbers, not equal proportions. Two other slips: dividing $35$ by the old total of $100$ to get 35% (option A, 35.75, is close to this), and treating a 25% price rise as a 25% cut in the number of marbles. The count falls to $100/1.25 = 80$ , not $75$ .

From the GATE 2018 EE paper. Every question of this paper · Download the full paper · All 58 Numerical questions, with notes

GATE 2018 EE GA Q.9: solution and answer

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