Explanation

Let x = 17d and y = 19d, where d is the HCF of x and y. Since 17 and 19 are coprime, LCM(x, y) = 17 × 19 × d = 323d. Setting 323d = 1615 gives d = 5. Hence x + y = 36d = 36 × 5 = 180, which is option B. A common error is to answer 36, the mere sum of the ratio terms, forgetting that the ratio must be scaled by the common factor d.