A, B and C can do a piece of work in 10 days, 20 days and 15 days respectively, working alone. How soon can the work be done if A assisted by B and C on alternate days?
A, B and C can do a piece of work in 10 days, 20 days and 15 days respectively, working alone. How soon can the work be done if A assisted by B and C on alternate days?
1). 10
2). \(6\frac{1}{3}\)
3). \(7\frac{1}{3}\)
4). 7
1 answers
A can complete the work in 10 days.
⇒ A’s 1day’s work = 1/10
B can complete the work in 20 days.
⇒ B’s 1 day’s work = 1/20
C can complete the work in 15 days.
⇒ C’s 1day’s work = 1/15
(A + B)’s 1 day’s work = (1/10) + (1/20) = 3/20 (A + B implies A and B)
(A + C)’s 1 day’s work = (1/10) + (1/15) = 1/6 (A + C implies A and C)
According to the question, A is assisted by B and C on alternate days.
⇒Their 2 day’s work = (3/20) + (1/6) = 19/60
[? (A + B) work on 1st day and (A + C) work on 2nd day]
⇒ Their (3 × 2 =) 6 day’s work = 3 × (19/60) = 57/60
⇒ Remaining work = 1 - (57/60) = 3/60 = 1/20
On 7th day (A + B) will work.
(A + B) do (3/20)th work in 1 day
⇒ Time taken by (A + B) to do remaining work = (1/3) days
∴ The work will get completed in = $(6 + \frac{1}{3} \Rightarrow 6\frac{1}{3})$ days