Let the distance to the top be d. therefore the speed of the man with escalator not moving \\\\(=(\\dfrac{d}{1}) m/min\\\\) therefore the speed of the escalator with the man at rest\\\\(=(\\dfrac{d}{3})\\\\)m/min when both the main and the escalator are moving, effective speed\\\\(= (\\dfrac{d}{3} +d)\\\\) m/min\\\\(= \\dfrac{4d}{3}\\\\) m/min Therefore time taken when both men and escalator are moving\\\\(= \\dfrac{distance}{speed} = \\dfrac{d}{\\dfrac{4d}{3}}\\\\)\\\\(\\dfrac{3}{4} min = 45\\\\)secondsHence (B) is correct answer