Answer: Option B
:
B
Swimming-S, Running-R, Cycling-c, Discus Throw-D and Horse Riding-H
From (i), (v) and (vi), Q won 2 gold medals but not in S or D.
From (iii), T won gold in one from among R or C while T did not win silver in S or D
From (i), S did not win silver in those events in which Q won gold medals. Hence, S did not win any medals in those events.
From (Iv), R won 4 medals and the other colleges won 3 or less medals.
So, the medals won by the remaining 4 colleges are 3, 3, 3 and 2.
T has won 2 medals (i.e., 1 gold and 1 silver (using iii).
P has won 3 medals. So, it must have won 1 gold in silver and 2 bronze in two from among R, C and H.
The gold medals are exhausted as P-1, Q-2, R-1, T-1,
S can win 3 medals: 2 silver and 1 bronze.
Q has won 3 medals: 2 gold among from R, C and H, an 1 bronze.
R won 4 medals: bronze in S, gold in D and 2 silver. There are only three Medal-winning combinations :
Table :- 1
$\begin{array}{ccccccc}& Swimming& Running& Cycling& DiscussThrow& HorseRiding& Total\\ P& G& B& B& X& X& 3\\ Q& X& G& G& B& X& 3\\ R& B& \frac{X}{S}& \frac{S}{X}& G& S& 4\\ S& S& X& X& S& B& 3\\ T& X& \frac{S}{X}& \frac{X}{S}& X& G& 2\end{array}$
Table:-2
$\begin{array}{ccccccc}& Swimming& Running& Cycling& DiscussThrow& HorseRiding& Total\\ P& G& B& X& X& B& 3\\ Q& X& G& X& B& G& 3\\ R& B& \frac{X}{S}& S& G& \frac{S}{X}& 4\\ S& S& X& B& S& X& 3\\ T& X& \frac{S}{X}& G& X& \frac{X}{S}& 2\end{array}$
Table :- 3
$\begin{array}{ccccccc}& Swimming& Running& Cycling& DiscussThrow& HorseRiding& Total\\ P& G& X& B& X& B& 3\\ Q& X& X& G& B& G& 3\\ R& B& S& \frac{X}{S}& G& \frac{S}{X}& 4\\ S& S& B& X& S& X& 3\\ T& X& G& \frac{S}{X}& X& \frac{X}{S}& 2\end{array}$