Question

A and B can do a work in 5 days. B and C can do work 7 days.A and C can do it in 4 days. Who among these will take the least time it put to do it alone?​

Answer 1

Answer:

A

Step-by-step explanation:

A will take least time to do the work alone

Answer 2

A+B ----------- 5 days

B+C-----------7 days

C+A-----------4 days

Total work = L.C.M of (5,7,4) = 140 unit

so, (A+B)'s 1 day work = 140/5 = 28 unit.....(1)

(B+C)'s 1 day work = 140/7 = 20 unit.....….....(2)

(C+A)'s 1 day work = 140/4 = 35 unit.............(3)

add (1)+(2)+(3)

(A+B)+(B+C)+(C+A) = 28+20+35

2(A+B+C) = 83 unit

(A+B+C)'s 1 day work = 83/2 unit ............(4)

put the value of (A+B) from (1) to (4)

28 + C = 83/2 => C = 83/2 - 28 = 27/2 = 13.5unit

in the same way-

from (4)&(2) -

A= 83/2 - 20 = 43/2 = 21.5 unit

from (4)&(3) -

B = 83/2 - 35 = 13/2 = 6.5 unit

Now we get everyone's 1 day work that are-

A's 1 day work = 21.5 unit

B's 1 day work = 6.5 unit

C's 1 day work = 13.5 unit

so, among A, B, C ,,

A does the highest work so he will take the least time to complete the task.