Complex Work Rate

[vineetbatra]

In a certain factory, each of a workers produce b pairs of shoes every c hours. If the workers work around the clock without any breaks, how many days are required to produce 1,000 pairs of shoes?

(A) 125c/3ab
(B) 1000c/ab
(C) 3a/125bc
(D) 3c/125ab
(E) 125ab/3c

The way I solve this problem,
it will take a*c man hours to produce b pairs of shoes. so for making 1 pair of shoes it will take ac/b man hours.

Now to make 1000 pair of shoes it will take 1000ac/b man hours. if I divide by number of workers i.e. a I will get man hours for all workers 1000ac/ba or 1000c/b

to get days, will divide the above equation by 24. that will give me 125c/3b, but I do not have that answer at all. OA a

Can someone please help me understand this Q.

[brick2009]

A workers --> b pairs in C hrs
A workers --> 1000 pairs in X hrs

If A = 1,

b--> c hrs
1000--> x hrs
=> x = 1000 * C / b HRS
= 1000/24 * C / b days
= 125/3 * C/B days
that is for 1 worker...for A workers...

X = 125/3 * C/(ba) --> A is the answer


Any other approaches..

[El Nino]

Each worker takes c hours to produce b pairs of shoes ==> hence, each worker produces b/c shoes per hour (e.g. 3 hours to produce 2 pairs of shoes = 2/3 shoes per hr)

a workers produce ab/c shoes per hour = 24ab/c shoes per day

1000 shoes will take 1000 / (24ab/c) days = 1000c / 24ab = 125c / 3ab

[vineetbatra]

Thanks guy, great explanation.