Problem Solving

Six M/C, each working at the same constant rate, together can complete a certain job in 12 days. How many additional m/c's, each working at the same constant rate, will be needed to complete a job in 8 days.

a) 2 b) 3 c) 4 d) 6 e) 8.

Can anyone please solve this question. I will post the OA soon.

Thanks.

Assume r = Rate of doing work for a machine

Rate x time = work

6r x 12 = 1 OR r = 1/72

Let number of machines be x
so x(1/72) . 8 = 1

x = 9.

So the number of additional machines = 9-6 = 3 (b)

Yes 3 is the correct answer. I am not sure how did you take the equation 6r X 12 = 1. I was not sure about the 6r part.

Lets look at it another way...

If it takes 12 days to do a job then the rate = 1/12 i.e. 1/12th of a job will be done in a day.

If 6 machines will perform 1/12th of a job in a day, then each machine will do 1/(12 x 6)th job a day

In the equation 6r = 1/12, so r = 1/72

think on it in an easy way

machines....job.....days..................so
6................ 1...... 12............... 6x1x12 = 72
?................ 1....... 8.................?x1x8=....?8

then 72/?8 = ................. ?=9

then 9-6=3(additional machines)
answ= b)

Kooooooooooooooolllllllllllllllllll man, andes1! Great approach indeed ...