A, B and C can do a work in 6, 8, 12 days respectively. B and C work t

Question

A, B and C can do a work in 6, 8, 12 days respectively. B and C work together for 2 days and then A takes C's place. How long will it take to finish the work?

A. 2 days
B. 3 days
C. 4 days
D. 5 days
E. 6 days

Chethan92 · Accepted Answer

Total work to be done = LCM(6,8,12) = 24 units
A can do 4 units per day
B can do 3 units per day
C can do 2 units per day

B+C in 1 day = 5 units
for 2 days, 10 units will be completed by B and C.
Remaining is 14 units.
Now A and B work together, They can do 4+3 = 7 units per day.
Then 14 units will be completed in 2 days.

A is the answer.

KSBGC · Answer

LCM method is suitable here.

LCM of 6,8,12 =24 units of work.

A's work = 4 units /day
B's work = 3 units/days
C's work = 2 units/day

(A + C)' 2 days work = 3 +2 = 5 *2 = 10 units.

Remaining Work = 24 - 10 = 14

14 Units done by (A + B)

(A + B)'s performance in a day = 4 + 3 =7

14/7 = 2 days.

Thus, A and B will take only 2 days to finish the remaining work .

A is the correct answer.

Archit3110 · Answer

rate of B & C = 1/8 + 1/12 ; 5/24
so amount of work done by b & c = 5/24 * 2 = 5/12
work left = 1-5/12 = 7/12

rate of work of A & B = 1/6+ 1/8 = 7/24
since 
w=r*t
w=7/12 , r = 7/24
t = 24/12 = 2

total work would be finished in 2 days of B& C and 2 days of A & B = 2+2 = 4
IMO C

thyagi · Answer

I just have one doubt... Is the question asking the total number of days or just the days in which A&b finish the remaining work. If it was total number of days then the answer is 4 days .
If the question is asking only the number of days it took A&b to finish the remaining work then the answer is 2 days ..... Which one is the right one. As far as I understood the question, it's asking about the days A&b finished the work, but OA is C.. 
Can anyone clear my doubt..

Posted from my mobile device

Archit3110 · Answer

thyagi 
question has asked  How long will it take to finish the work?

which means total days..

nide · Answer

if given n people finishing a work in k days 1/a + 1/b + 1/c + 1/d + .... + 1/n= 1/k (i.e., 1/k th fraction of work done on each day) given : 1/a = 1/6 1/b = 1/8 1/c = 1/12 b and c work together for two days each day 1/b+1/c two days 2*(1/b+1/c) a replaces c a and b works for say t days t*(1/a+1/b) the sum all the fractions work done should be one 2*(1/b+1/c) + t*(1/a+1/b) = 1 2*(1/8 + 1/12) + t*(1/6+1/8) = 1 1/4+1/6+7t/24 = 1 5/12 + 7t/24 = 1 7t/24 = 1- 5/12 = 7/12 t = 2 days if the question is asking about the amount of time taken to finish the work after A replaces C Option A - 2 days if the question is asking for the total time taken to finish the work 2 + 2 = 4 days Option C - 4 days ---------------------------------------------------------------- please leave a kudos

GmatKnightTutor · Answer

Fundamentally, people, you're going to have to understand the concept at play here. I can understand (believe me) the desire to just plug the variables into some formula, get the answer, and move on. Try and fight it, people.

First, you need to thoroughly understand how much work each person is doing. If I ask you how much work, as in the fraction of work, A does in 1 day, you should immediately go That's easy! -- It's 1/6th.

The rest is frankly quite simple. Just a bit of addition and some algebra.

---2 days of B and C + X days of C and B = 1 block of Work

----2( 1/8 + 1 /12 ) + x (1/6 + 1/8 ) = 1

Just be careful you add X and 2, since it's the total number of days you want to get!

fireagablast · Answer

Question is worded confusingly. It takes 2 days to "finish" the work that had been started for two days, totaling 4 days.

1 = (1/8+1/12)(2) + (1/8+1/6)t
28 = 14t
t=2

2+2 = 4 days total

premsmit · Answer

It is not clear, they want "total time" or "remaining time" to complete the work. Vague question.

Palladin · Answer

When the question asks how long will it take to finish the work, B and C have already worked for 2 days.
Wouldn't the answer be the time worked by A and B together then?

MV94 · Answer

On the test, is GMAC going to be this vague about whether the question is regarding remaining time vs. total time? It seems between the above question and this question ( https://gmatclub.com/forum/pump-a-can-empty-a-pool-in-8-minutes-pump-b-can-empty-a-pool-in-6-min-283543.html ) the objective isn't entirely clear. In both cases my math was right, but I had trouble interpreting what the question was asking for.

bumpbot · Answer

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