AP DSC School Assistant Math Model Test 2

Concept:The work is done collectively by pairs of workers. To find the time for one worker alone, we first find the combined work rate of all three together, then subtract the rate of the pair that does not include that worker.Explanation:Let the total work be the Least Common Multiple (LCM) of the given days: 12, 15, and 20. The LCM is 60 units.Calculate work done per day by each pair:Work done by (A + B) in 1 day = $\frac{60}{12} = 5$ units.Work done by (B + C) in 1 day = $\frac{60}{15} = 4$ units.Work done by (A + C) in 1 day = $\frac{60}{20} = 3$ units.Add the work of all three pairs:$(A+B) + (B+C) + (A+C) = 5 + 4 + 3 = 12$ units per day.This sum equals $2(A+B+C)$, so work done by (A+B+C) together in 1 day = $\frac{12}{2} = 6$ units.Now, to find A’s individual work per day, subtract the work of (B+C) from the total of all three:A’s 1 day work = $(A+B+C) - (B+C) = 6 - 4 = 2$ units.Thus, time taken by A alone to complete 60 units = $\frac{60}{2} = 30$ days.Answer:30 days (Option C).