GATE CE 2020 Set 2 — Question 10

The question provides a pie chart for the monthly distribution of LED bulbs sold from January to June 2018 and a table for the ratio of bulbs sold by firms X and Y.From the pie chart, the percentages of bulbs sold in the months of April, May, and June are:

• April: $15\%$
• May: $10\%$
• June: $10\%$

Total percentage for April-June = $15\% + 10\% + 10\% = 35\%$.Let $T$ be the total number of bulbs sold from January to June. According to the question, the total bulbs sold during April-June is $50,000$. Thus:
$0.35T = 50,000 \implies T = \frac{50,000}{0.35} \approx 142,857.14$Now, calculate the bulbs sold by firm Y in these months using the given ratios $(X : Y)$:

• April ($3 : 2$): $Y_{\text{April}} = \frac{2}{3+2} \times 15\% \text{ of } T = 0.4 \times 0.15T = 0.06T$
• May ($1 : 4$): $Y_{\text{May}} = \frac{4}{1+4} \times 10\% \text{ of } T = 0.8 \times 0.10T = 0.08T$
• June ($9 : 11$): $Y_{\text{June}} = \frac{11}{9+11} \times 10\% \text{ of } T = 0.55 \times 0.10T = 0.055T$

Total bulbs sold by Y during April-June = $(0.06 + 0.08 + 0.055)T = 0.195T$.
Substituting $T$: $0.195 \times \frac{50,000}{0.35} \approx 27,857.14$.None of the options match this result. However, if we assume the "total number of bulbs" ($50,000$) refers to the entire period from January to June ($T = 50,000$):
Total bulbs sold by Y = $0.195 \times 50,000 = 9,750$.This matches option (B). Due to the ambiguity in the problem statement (whether $50,000$ refers to the April-June total or the Jan-June total), the question was marked as Marks to All (MTA) in the official answer key.