Question

How many "Rank 1" votes did West Indies get?

• A. 83
• B. 82
• C. 81
• D. 80

Answer 1

The correct option is B

82

Let the number of "First Rank” votes of Australia and West Indies be equal to c and d respectively.

The "First Rank” votes of India, England. Australia and West Indies should add up to 350.

Therefore, 101 + 84 + c + d = 350 , c + d = 165 , c = 165 - d

Now, 84 $>$ c $>$ 165 - c

Therefore c = 83 and d = 82. Hence, (b)

After the second round of counting,

India's vote - count = India's "First Rank” votes + West Indies's "First Rank” votes that have India as "Second Rank” = 101 + 17 = 118

Let the number of West Indies's "First Rank” votes that have England and Australia as the "Second Rank” be x and y respectively.

Therefore, 17 + x + y = 82 y = 65 - x.

England's vote-count = England's "First Rank” votes + West Indies's "First Rank” votes that have England as the "Second Rank” = 84 + x.

Australia's vote-count = Australia's "First Rank” votes + West Indies's "First Rank” votes that have Australia as the "Second Rank” = 83 + y = 83 + 65 - x = 148 - x.

As India led while England was eliminated.

118 $>$ 148 - x $>$ 84 + x , x = 31.

Therefore, 31 of West Indies's "First Rank” votes have England as the "Second Rank”.