(a)(i)
(ii) \(21 + 4 + 5 + 10 + x + 35 - x + 32 - x = 100\)
\(107 - x = 100\)
\(x = 107 - 100 = 7\)
Therefore, 7 traders sell oranges and mangoes alone.
(b) \(312_{four} + 52_{x} = 96_{ten}\)
\(312_{4} = 3 \times 4^{2} + 1 \times 4^{1} + 2 \times 4^{0}\)
= \(48 + 4 + 2 = 54_{10}\)
\(52_{x} = 5 \times x^{1} + 2 \times x^{0}\)
= \((5x + 2)_{10}\)
\(\therefore 54 + (5x + 2) = 96\)
\(56 + 5x = 96 \implies 5x = 96 - 56 = 40\)
\(x = 8\)
\(\therefore 312_{4} + 52_{8} = 96_{10}\)