Question

A and B can complete a work in 6 days. B and C can complete the same work in 8 days. C and A can complete in 12 days. How many days will take for A, B and C combined together to complete the same amount of work ?​

Answer 1

Answer:

73.6 days

Step-by-step explanation:

Let A can complete whole work in x days

Let B can complete the same work in y days

Let c can complete the whole work in z days

=In x days A can complete the whole work (1)

x days =1 part

1 days = 1/x part

In 6 days = 6/x part

In y days B can complete the whole work

y days = 1 part

1 days = 1/y part

6 days = 6/y part

According to the question A and B can complete the whole work in 6 days

= 1/x + 1/y= 6

6/x + 6/y= 1

According to the question B and C can complete the whole work in 8 days

8/y+ 8/z=1

According to the question A and C can complete the whole work in 12 days

12/x+12/z= 1

Let 1/x = p ,1/y= q and 1/z = r

6p+ 6q = 1

8q+8r=1

12p+12r= 1

:p=1-6q/6

:r=1-8q/8

putting tese values in eq....3

12-72q/6+12-96q/8=1

q=5/48

similarly,r= 1/48 and p= 1/16

1/x=1/16

and x = 16, 1/y = 5/48 and y = 9.6

1/48= 1/z, and z = 48

Hence ABC, together can complete the same work= sum of x,y and z= 48+16+9.6=73.6 days ✓ Ans