For making a table it needs human labour 3 times the labour

Work of making 1 table = 3 * Work of making 1 bench
Work of making 5 tables = Work of making 15 benches
Work of making 8 tables = Work of making 24 benches

6 workers...........36 benches+15 benches = 51 benches..............12 days
10 workers.........61 benches + 24 benches = 85 benches.............?? days

No of days = 12 * (6/10) * (85/51) = 12days

Use the following formula:
\(\frac{(workers)(time)}{output} = \frac{(workers)(time)}{output}\)

Let each bench = 1 pound and each table = 3 pounds (implying 3 times the labor).

Output 1: 36 benches and 5 tables = 36*1 + 5*3 = 51 pounds.
Output 2: 61 benches and 8 tables = 61*1 + 6*3 = 85 pounds.

Since 6 workers take 12 days for Output 1, and we must determine the time needed by 10 workers for Output 2, we get:
\(\frac{6*12}{51} = \frac{10t}{85}\)
\(\frac{2*12}{17} = \frac{2t}{17}\)
\(12 = t\)

Hello GmatGuruNy,

Can you please explain how is that formula derived or any alternate way.

I tried maintaining bench and table work in equal units and then keeping effort and days on one side and then used the unitary approach for work and effort.

\(\frac{(workers)(time)}{output} = \frac{(workers)(time)}{output}\)

Numerator:
Workers and time are INVERSELY PROPORTIONAL.
If the number of workers doubles, the time required to produce the same output is cut in half.
Values that are inversely proportional MULTIPLY to yield a constant value:
(workers)(time) = k

Denominator:
Workers and output are DIRECTLY PROPORTIONAL.
If the number of workers doubles, the output also doubles.
Time and output are also DIRECTLY PROPORTIONAL.
If the time triples, the output also triples.
Values that are inversely proportional DIVIDE to yield a constant value:
\(\frac{workers}{output} = k\)
\(\frac{time}{output} = k\)

Putting it all together, we get:
\(\frac{(workers)(time)}{output} = k\)

Thanks GMATGuru!!

It's very clear

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.