maths

Please guide me to solve the below problem:

'A'an do 2/3 of a work in 40 days.'B'can do 1/2 of the work in 75 days.'C'can do 3/4of work in 75 days.If all them together work in how many days will they do 5/6 0f the work.

I had solved the above problem like this:

A can do the work=3/2*40=60 days.
A's one day work =1/60

B can do the work=2/1*75=150 days
B's one day work=1/150

C can do the work=4/3*75=100 days.
C's one day the work=1/100

They together=1/60+1/150+1/100
=5+2+3/100
=10/300=1/30
They complete the 5/6 of the work =1/30*5/6
=1/36

Therefore ,they complete the 5/6 of the work in 36 days.

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  1. Here is another way:

    rate=rate1+rate2+rate3
    = W/60+W/150+W/100= W(5+2+3)/300
    = W/30 check same as yours.
    So time= amountwork/rate= 5W/6 /(W/30)

    time= 150/6=25 days

    So our answers are different, check mine, then yours.I don't agree with how you get 1/36, time= work/rate, not multiplied

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