The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees. Which item among the following has generated the maximum revenue per kg? [Exports pie chart: Item 1: 14%, Item 2: 20%, Item 3: 35%, Item 4: 6%, Item 5: 2%, Item 6: 12%, Item 7: 4%, Item 8: 7%] [Revenues pie chart: Item 1: 17%, Item 2: 9%, Item 3: 14%, Item 4: 35%, Item 5: 14%, Item 6: 3%, Item 7: 4%, Item 8: 4%] A. Item 2 B. Item 3 C. Item 6 D. Item 5

GATE 2014 · General Aptitude · Pie Chart · medium

Answer: Item 5 generates the maximum revenue per kilogram with a ratio of 7.0 (revenue % to quantity %), far exceeding all other options. Answer: D. Item 5.

  1. Set up the revenue-per-kg formula for comparison: Since Rev/kg_i = (rev_i% x Total_Rev) / (qty_i% x Total_Qty), and Total_Rev / Total_Qty is the same for all items, only the ratio (rev_i% / qty_i%) matters for comparison.
  2. Compute ratio for Item 2: Item 2: qty = 20%, rev = 9%. Ratio = 9/20 = 0.45.
  3. Compute ratio for Item 3: Item 3: qty = 35%, rev = 14%. Ratio = 14/35 = 0.40.
  4. Compute ratio for Item 6: Item 6: qty = 12%, rev = 3%. Ratio = 3/12 = 0.25.
  5. Compute ratio for Item 5: Item 5: qty = 2%, rev = 14%. Ratio = 14/2 = 7.00.
  6. Verify with actual values: Revenue from Item 5 = 35 crore Rs. Quantity of Item 5 = 10,000 tonnes = 1,00,00,000 kg. Rev/kg = 35,00,00,000 / 1,00,00,000 = 35 Rs/kg.