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If X can complete a task in 10 days and Y in 15 days, in how many days can they complete the task working together?
5 days
6 days
7 days
8 days
6 days
Assume total work is the LCM of 10 and 15, which is 30 units. Find individual efficiencies and divide total work by combined efficiency.
X can complete the task in 10 days and Y can complete it in 15 days.
T=x+yx├ЧyтАЛ
Assume total work is the LCM of 10 and 15, which is 30 units. Find individual efficiencies and divide total work by combined efficiency.
Adding the number of days directly (10 + 15 = 25) instead of adding their daily work rates or using the LCM method.
Identify Individual Work Rates
The work done by X in 1 day is 101тАЛ and the work done by Y in 1 day is 151тАЛ.
WXтАЛ=101тАЛ,WYтАЛ=151тАЛ
Calculate Combined 1-Day Work
Add the individual 1-day work rates of X and Y to find their combined work rate per day.
Combined┬аWork=101тАЛ+151тАЛ=303+2тАЛ=305тАЛ=61тАЛ
Determine Total Time Taken
Take the reciprocal of the combined 1-day work to find the total number of days required to complete the task together.
T=61тАЛ1тАЛ=6┬аdays
B is correct because working together they complete the task in 6 days.
This concept is directly applicable to Pipes and Cisterns problems where filling and emptying rates replace worker efficiencies.
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