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 exactly 12 days . if b starts , they take half 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 = 6 no . of days when b works = 6 → 6 x + 6 y = 1 when b starts : no . of days when a works = 6.5 no . of days when b works = 5.5 → 6.5 x + 5.5 y = 1 solving the above two equations for xy x = 1 / 12 y = 1 / 12 → total work done by ab in a day = 1 / 12 + 1 / 12 = 2 / 12 = 1 / 6 → no . of days to complete the work when both work together = 6 answer : c"
inverse(add(inverse(subtract(12, const_1)), inverse(add(12, 2))))