In a factory, 30 identical machines working together can manufacture

Question

In a factory, 30 identical machines working together can manufacture a batch of parts in 2 hours. Initially, 20 machines began working, and after 1.5 hours, 20 identical backup machines joined them. Will it take less than 0.75 hours for all the machines together to finish manufacturing the batch?

(1) The rate of a backup machine is lower than the rate of an original machine.

(2) 60 backup machines working together can manufacture the same batch of parts in 2 hours.

Bunuel · Accepted Answer

Official Solution:

In a factory, 30 identical machines working together can manufacture a batch of parts in 2 hours. Initially, 20 machines began working, and after 1.5 hours, 20 identical backup machines joined them. Will it take less than 0.75 hours for all the machines together to finish manufacturing the batch?

Assuming each machine completes 1 unit of work in 1 hour, the total work would be 30 * 2 = 60 units. In 1.5 hours, 20 machines would complete 20 * 1.5 = 30 units of work. In the next 0.75 hours, they would complete 20 * 0.75 = 15 units of work, leaving 60 - 30 - 15 = 15 units. So essentially, the question boils down to whether 20 backup machines can complete 15 units of work in 0.75 hours.

(1) The rate of a backup machine is lower than the rate of an original machine.

We know that 20 original machines can complete 20 * 0.75 = 15 units of work in 0.75 hours. Since the backup machines are slower, 20 backup machines would complete less than 15 units of work in 0.75 hours. This is exactly what we needed to check. Sufficient.

(2) 60 backup machines working together can manufacture the same batch of parts in 2 hours.

This was the only missing piece from the stem. Now, we know everything, and there is no need to calculate anything for this statement. From the stem, we know the rate and number of original machines involved, and the size of the work to be done. From this statement, we know the rate of the backup machines. We also know all the relevant time values given in the question. Therefore, we can surely answer any question about this setup. Sufficient.

Answer: D

ravi1522 · Answer

Hello,
Let assume Rate of original as X
Let assume Rate of backup as X1

so total work done will be =30*X*2=60X
Now 20 machine worked for 1.5 hours 
so total work remaining will be =60X-1.5*20*X=30X
Now additional backup machine is added
time required =30X/(20X+20X1)
if the rate is same the time will be 0.75 hours
Statement 1
says that backup is slower than original so together they will take more time than 0.75 hours

Sufficient 
Statement 2
It also says that the backup will be slower so together they will take more time than 0.75 hours 
So correct option is D
Both statement sufficient

I hope it helps

ODST117 · Answer

Rate of work of  30  original machines =  \frac{1}{2} 
Rate of work of  1  original machine =  M  =  \frac{1}{2*30}  =  \frac{1}{60}

The question states, initially,  20  original machines worked for  1.5  hours. We know the rate of work of  1  original machine  M .
Therefore, the work done by these  20  original machines in  1.5  hours is  20*(M)*1.5 = 20*(\frac{1}{60})*3/2 = \frac{1}{2}  units of work.
So,  \frac{1}{2}  of the work is remaining.
At this point they brought in  20  backup machines to work along with the  20  original machines. Can these  40  machines complete the remaining work in less than  0.75  hours?

Statement 1:    The rate of a backup machine is lower than the rate of an original machine.

Let the rate of work of a backup machine be  B . This statement says  B<M . Let's see how much time is required for the  40  machines to complete  \frac{1}{2}  of the work if  B = M . Time is  x  hours.

(20M + 20B)x = \frac{1}{2}

40(\frac{1}{60})x = \frac{1}{2}

x = 0.75

If  B = M , the time taken to complete the remaining work would be exactly  0.75  hours. If  B<M , then time taken would obviously be more than  0.75  hours.

Therefore, Statement 1 is sufficient.

Statement 2:    60 backup machines working together can manufacture the same batch of parts in 2 hours.

With this statement, we can find what B is.

60B*2 = 1

B = 1/120

At this point you can plug in the value of  B  and  M  into  (20M + 20B)x = \frac{1}{2}  to find what  x  will be.
 But, as we have already proved with Statement 1, if  B<M,  then time taken to complete the remaining work is more than  0.75  hours. Here,  B  is less than  M  ( \frac{1}{120}<\frac{1}{60} ).

Therefore, Statement 2 is sufficient.

Final answer: D (EACH statement ALONE is sufficient)

Bunuel · Answer

Similar tricky question to practice: https://gmatclub.com/forum/in-a-print-s ... 44406.html

In a factory, 30 identical machines working together can manufacture

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