working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exact 8 days . if b starts , they take a day more . how long does it take to complete the task if they both work together ?
"work done by ab in a day = xy respectively . when a starts : no . of days when a works = 4 no . of days when b works = 4 → 4 x + 4 y = 1 when b starts : no . of days when a works = 5 no . of days when b works = 3 → 5 x + 3 y = 1 solving the above two equations for xy x = 1 / 8 y = 1 / 8 → total work done by ab in a day = 1 / 8 + 1 / 8 = 1 / 4 → no . of days to complete the work when both work together = 4 answer : d"
inverse(add(inverse(subtract(8, const_1)), inverse(add(8, 2))))