A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
A) 11 days
B) 12 days
C) 13 days
D) 14 days
Answers
Solution
Given :-
- A, B and C can do a piece of work in 24 days, 30 days and 40 days
- They began the work together but C left 4 days before the completion of the work
Find:-
- Work complete days .?
Explanation
We Have,
★ Working days of A = 24 days
★ working days of B = 30 days
★ Working days of C = 40 days
Then,
==> 1 days work of A , B & C = 1/24 + 1/30 + 1/40
==> 1 days work of A , B & C = ( 5 + 4 + 3)/120
==> 1 days work of A , B & C = 12/120
==> 1 days work of A , B & C = 1/10
According to question,
C left 4 days of before completion of work , thats means only A & B work during the last 4 days .
So,
==> Work done by A & B during the last 4 days = 4(1/24 + 1/30)
==> Work done by A & B during the last 4 days = 4(5+4)/120
==> Work done by A & B during the last 4 days = 4 × 9/120
==> Work done by A & B during the last 4 days = 3/10
So,
Remaining Work = 7/10,
which was done by A,B and C in the initial number of days.
And,
==> Number of days required for this initial work = 7 days.
Thus,
The total numbers of days required = 4 + 7 = 11 days.
Hence
- Required number of days will be = 11 days.
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