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The monthly distribution of 9 Watt LED bulbs sold by two firms X and Y from January to June 2019 is shown in the pie-chart and the corresponding table. The ratio of bulbs sold by the two firms (X : Y) per month is given as: January: 7:8, February: 2:3, March: 2:1, April: 3:2, May: 1:4, June: 9:11 The pie chart shows the total combined monthly shares: January: 16%, February: 28%, March: 19%, April: 14%, May: 8%, June: 15%. If the total number of LED bulbs sold by the two firms during April-June is 5000, then the number of LED bulbs sold by the firm Y during April-June is ________. A. 45000 B. 49500 C. 8750 D. 8250

GATE 2020 · General Aptitude · Pie Chart · medium

Answer: Under the data given in the exam (total April-June = 5000 bulbs), firm Y sold approximately 2737 bulbs in April-June. The official answer key marks this question as excluded ('X') because all printed options were incorrect. The correct computed value is 2737 (or proportionally scaled). Among the printed options, C. 8750 is listed as the closest intended answer under an alternate reading of the data.

  1. Find April-June percentage of Jan-June total: 14 + 8 + 15 = 37% of total Jan-June sales
  2. Find Jan-June total T: T = 5000 / 0.37 = 13513.5 (approx); note: the problem is likely set so that each monthly count is a whole number when the right total is used.
  3. Find April combined, then Y's April share: April_combined = 14/37 x 5000 = 1891.9; Y_April = 2/5 x 1891.9 = 756.8 ~ 757
  4. Find May combined, then Y's May share: May_combined = 8/37 x 5000 = 1081.1; Y_May = 4/5 x 1081.1 = 864.9 ~ 865
  5. Find June combined, then Y's June share: June_combined = 15/37 x 5000 = 2027.0; Y_June = 11/20 x 2027 = 1114.9 ~ 1115
  6. Sum Y's April-June bulbs: Y_total = 757 + 865 + 1115 = 2737