A and b can complete a work in 8 days working together. b alone can do it in 12 days after working for four days, b left the work how many days will a take to complete the remaining work?
Answers
Given :-
- A and B can complete a work in 8 days working together.
- B alone can do it in 12 days ..
- After working for four days, B left the work .
To Find :-
- How many days will a take to complete the remaining work ?
Solution :-
LCM of 8 & 12 = 24 unit = Let Total work.
So,
→ Efficiency of (A + B) = (Total work) / (Total No. of Days.) = (24/8) = 3 units/day.
Similarly,
→ Efficiency of B = (Total work) / (Total No. of Days.) = (24/12) = 2 units/day.
Hence,
→ Efficiency of A = Efficiency of (A + B) - Efficiency of B = 3 - 2 = 1 unit/day.
Now, it has been said that, both work together for four days.
So,
→ in 4 days both (A + B) completes = Efficiency of (A + B) * No. of Days. = 3 * 4 = 12 units .
Than,
→ work left to be done = 24 - 12 = 12 units.
Now, we have given that, B left the work. Therefore, we can say that, rest 12 unit of work was done by A alone.
Hence,
→ Remaining work = 12 units.
→ Efficiency of A = 1 unit/day.
→ Time taken by A = (Remaining work) / (Efficiency of A) = (12/1) = 12 days. (Ans.)
∴ A complete the remaining work in 12 days.
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