a+b can do piece of work in 12 days , b+c can do piece of work in 10 days, c+a can do piece of work in 15 days, find the time taken by a+b+c together to complete can work in how many days??
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a+b ==== 12
b+c ==== 10
c+a ====15
take the L.C.M of 12,10,15 = 60.
total work = 60 unit
so 1 day work of a+b = 60/12= 5
1 day work of b+c = 60/10 = 6
1 day work of c+a = 60/15 = 4
total work of (a+b+b+c+c+a) = 5+6+4
2(a+b+c)=15 ,
one day work of (a+b+c)= 15/2
total work is 60 unit so day required
= (60)/(15/2) = (60×2)/15 = 4×2 = 8 days.
b+c ==== 10
c+a ====15
take the L.C.M of 12,10,15 = 60.
total work = 60 unit
so 1 day work of a+b = 60/12= 5
1 day work of b+c = 60/10 = 6
1 day work of c+a = 60/15 = 4
total work of (a+b+b+c+c+a) = 5+6+4
2(a+b+c)=15 ,
one day work of (a+b+c)= 15/2
total work is 60 unit so day required
= (60)/(15/2) = (60×2)/15 = 4×2 = 8 days.
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