Question

A and b can complete a work in 12 days together, b and c can complete the same work in 15 days together and a and c can complete that work in 20 days together. in how many days a can complete the same work alone?

Answer 1

they can complet the work in 15 days

Answer 2

Complete the same work alone is :

A + B complete a piece of work in 12 days

B + C complete a piece of work in 15 days

C + A complete a piece of work in 20 days

 First we take LCM of these numbers 12 ,  15 , 20

so,                        

                                LCM is 60                            ( total work is 60 )

A + B complete whole work in 12 days and total work is 60

then (A + B) complete work in 12 day = 60/12 = 5    (efficiency of A + B )

B + C complete whole work in 15 days and total work is 60

then ( B + C ) complete work in  15 day = 60/15 = 4     (efficiency of B+C )

C + A complete whole work in 20 days and total work is 60

then ( C + A ) complete work in 20 day = 60/20 = 3     (efficiency of C+A )

now ,

• Efficiency of ( A + B ) is 5
• Efficiency of ( B + C ) is 4
• Efficiency of ( C + A ) is 3             

          

now ,    ( A + B ) + ( B + C ) + ( C + A ) = 5 + 4 + 3 = 12

                          A + B + B + C + C + A = 12  

                                 2A + 2B + 2C = 12    

                               A + B + C = 12/2    =  6

Now , we know the efficiency of B + C = 4 , this value put in A + B + C ...

                                    A + B + C = 6

                                       A + 4 = 6

                                          A = 2            (efficiency of A )

now , we know that              C + A = 3

                                              C + 2 = 3       ( A = 2 )

                                          C = 1            (efficiency of C )    

now , we know that              B + C = 4

                                              B + 1 = 4       ( C = 1 )

                                             B = 13            (efficiency of B )  

 so ,                             total work  = 60

now, A complete whole work alone  ,     60/2 = 30 days

        B complete whole work alone  ,     60/3 = 20 days

        C complete whole work alone  ,     60/1 = 60 days

                            

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