AB can do the work in 12 days B C in 15 days and AC in 20 days . in how many days they will finish the work together and separately.
Answers
Given,
A and B and can do a piece of work in 12 days.
B and C do it in 15 days.
C and A do it in 20 days.
(A + B)'s one day work = 1/12
(B + C)'s one day work = 1/15
(C + A)'s one day work = 1/20
(A + B) + (B + C) + (C + A)
= 1/12 + 1/15 + 1/20
= 2(A + B + C) = (5 + 4 + 3)/60
= A + B + C = 12/(30 × 2) = 1/5
A's one day work ⇒
= (A + B + C) - ( B + C)
= 1/5 - 1/15
= (3 - 1)/15
= 2/15
B's one day work ⇒
= (A + B + C) - (A + C)
= 1/5 - 1/20
= (4 - 1)/20
= 3/20
C's one day work ⇒
= (A + B + C) - (A + B )
= 1/5 - 1/12
= (12 - 5)/60
= 7/60
Question :
AB can do the work in 12 days B C in 15 days and AC in 20 days . in how many days they will finish the work together and separately.
Answer :
A will do the work in 2/15 days, B will do the work in 3/20 days and C will do the work in 7/60 days.
Step-by-step explanation :
A and B and can do a piece of work in 12 days.
B and C do it in 15 days.
C and A do it in 20 days.
(A + B)'s one day work = 1/12
(B + C)'s one day work = 1/15
(C + A)'s one day work = 1/20
⇒ (A + B) + (B + C) + (C + A)
⇒ 1/12 + 1/15 + 1/20
⇒ 2(A + B + C) = (5 + 4 + 3)/60
⇒ A + B + C = 12/(30 × 2) = 1/5
A's one day work -
⇒ (A + B + C) - ( B + C)
⇒ 1/5 - 1/15
⇒ (3 - 1)/15
⇒ 2/15
B's one day work -
⇒ (A + B + C) - (A + C)
⇒ 1/5 - 1/20
⇒ (4 - 1)/20
⇒ 3/20
C's one day work -
⇒ (A + B + C) - (A + B )
⇒ 1/5 - 1/12
⇒ (12 - 5)/60
⇒ 7/60