Three machines, K, M, and P, working simultaneously and

I believe that you have already figured that I is sufficient.

In st#2 - you can find "m". But now where do you put this value to figure out K?

St 1 alone is sufficient

Responding to a pm:

We know that the rate of work of all 3 together is 1/24 i.e. they complete 1/24 of the work every minute.

To know how long machine K will take alone, we need to know the rate of work of machine K (i.e. how much work does machine A alone do every minute).

(I) We know how much work machines M and P do together every minute. They do 1/36 of the work. When all three work together, they complete 1/24 of the work. How does the 1/24 - 1/36 = 1/72 of the work? Of course machine K does it. So this gives us the rate of work of mahcine K and hence time taken by machine K alone = 72 mins. Sufficient

(II) Machines K and P together complete 1/48 of the work every minute. The problem is, out of this 1/48, how much does machine K do? We don't know. Not sufficient.

Answer A


or assume the work to be 72 units. All three machines together complete it in 24 mins so they do 3 units per min.

(I) M and P together complete 72 units in 36 mins so they make 2 units per min. Hence machine K makes 1 unit per min and will take 72 mins to complete 72 units.
(II) Machines K and P complete 72 units in 48 mins so they make 72/48 units per min, But how many does K make out of them? We don't know.

Answer (A).
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Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?

Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \(\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}\).

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes --> \(\frac{1}{m}+\frac{1}{p}=\frac{1}{36}\), thus \(\frac{1}{k}+\frac{1}{36}=\frac{1}{24}\) --> we can find the value of \(k\). Sufficient.

(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes --> \(\frac{1}{k}+\frac{1}{p}=\frac{1}{48}\). The value of k cannot be determined from the data we have. Not sufficient.

Answer: A.

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