As second one works twice as fast as the first, working together second will do 2/3 of work and the first 1/3 of work (their ratio 1/2).

Answer: D.
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I solved it this way:

Step 1:

In one hour, the amount of work completed by Machine 1 is 1/8 and the amount of work completed by Machine 2 is ¼ i.e. Machine 2 works twice as fast as Machine 1.

(You can get the answer in Step 1 only. Anyhow, you will understand how to get the answer in the Step 1 by using a shortcut in Step 3)


Step 2:

In two hours, the amount of work completed by Machine 1 is 2/8 and the amount of work completed by Machine 2 is 2/4.

⇨ Total work completed in 2 hours by 2 machines = (2/8)+(2/4) => (1/4) + (1/2) => 0.25+0.50 = 0.75.
⇨ So the total amount of work completed by both the machines is 75 %. Out of the 75%, Machine 1 completes 50% of the work and Machine 2 completes 25% of the work.


Step 3:

Only 25% of the work is left. So the remaining work has to be divided between Machine 1 and Machine 2. As we know, Machine 2 can do the work twice as fast as Machine 1.

For example, if Machine 1 can do 10% of the work, Machine 2 can do 20% of the work in the same time. So, together they will complete 30% of the work. So from this example, we can understand that any work can be divided into 3 parts, and if Machine 1 completes 1 part of the work, and Machine 2 completes 2 parts of the work in the same time, irrespective of the quantum of work.

Now, the pending work is 25%. Let’s divide the work into 3 equal parts i.e. 8.33% per part. So, Machine 1 will complete 8.33% of the work whereas Machine 2 will complete 16.66% of the work, which is remaining.

So the total work completed by Machine 1 = 25%+8.33% = 33.33%
The total work completed by Machine 2 = 50% + 16.66% = 66.66%

So, the answer is (D)

We can apply Step 3 in Step 1 to get the solution faster, avoiding all the unnecessary calculations of Step 2 and Step 3.

Prefer Bunuel's approach

As the second machine works twice as fast as does the first one, the second machine will do twice as much work as does the first one. Together, if they complete a job, the second machine has worked twice as much as has the first machine.
Thus, work done by second machine relative to the total work done is 2/3 => 66.67%
Answer: D
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