Concept: The question tests on the area of Probability
Since it is a question on conditional probability, we can use Bayes Theorem.
By Bayes Theorem, P( A given B) = P(A / B) = P( A and B) / P(B)
Therefore P(Right Handed given that he hits the target) = P(RH and Hits) / P(Hits)
There are 8 Left handed and 12 Right handed archers.
P(Left Handed) = 8/20 = 2/5 = 0.4 and P(RH) = 3/5 = 0.6
P(Hitting the target and LH) = 0.4 * 0.7 = 0.28
P(Hitting the target and RH) = 0.6 * 0.9 = 0.54
P(Hitting the target) = P(Hitting the target and LH) + P(Hitting the target and RH) = 0.28 + 0.54 = 0.82
Therefore the required probability = 0.54 / 0.82 = 27/41