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X and Y can complete a piece of work in 8 days and 12 days, respectively. If they work on alternate days, with X working on the first day, how long wi
Question

X and Y can complete a piece of work in 8 days and 12 days, respectively. If they work on alternate days, with X working on the first day, how long will it take them to complete the same work?

A.

9129\frac{ 1}{2}​ days

B.

9359\frac{ 3}5 ​days

C.

9239\frac{ 2}3​ days

D.

9259\frac{ 2}5 ​days

Correct option is A

Given:
X can complete the work in 8 days.
Y can complete the work in 12 days.
They work on alternate days, with X starting on the first day. 
Formula Used: 
Total work = Efficiency ×\times Time
Solution: 
Total work  = LCM of 8, 12 = 24 unit

Efficiency of X = 248\frac{24}{8}​ = 3 days 

Efficiency of Y = 2412\frac{24}{12}​ = 2 days 

As they work alternate starting with X 
So, in two days X and Y work = 3 + 2 = 5 
In 8 days , total work completed = 5 ×\times 4 = 20 unit
Now, X work for 9th day ,
total work done = 23 unit 
Y complete the remaining work = 12 days\frac{1}{2} \, days 
Total time = 9+12=912 days9+\frac{1}{2} = 9\frac{1}{2} \, days​​

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