The time taken by ‘A’ to build a wall alone is 50% more than the time taken by him to build it along with ‘B’. ‘B’ will take how much percent more time to build the same wall than the time taken by him to build it along with ‘A’?

Solution

Let the work ‘A’ and ‘B’, can do in 1 day be ‘a’ units and ‘b’ units, respectively. Let they takes ‘p’ days to build the wall, together Therefore, Total work = (a + b) × p units …….. (1) According to the question, Time taken by ‘A’ to build the wall alone = 1.5p days Therefore, total work = 1.5p × a units….. (2) From equation (1) and (2), we get 2b = a Therefore, total work to be done = (a + b) × p = 3bp units Time taken by 'B' to build the wall = 3bp/b = 3p days Therefore, required percentage = (3p – p)/p} × 100 = 200% more time