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

Question

For making a table it needs human labour 3 times the labour needed to make a bench. 6 workers can make 36 benches and 5 tables in 12 days. How many days will 10 worker need to make 61 benches and 8 tables?

A. 6
B. 8
C. 10
D. 12
E. 18

Show Answer

Official Answer

D

A. 6
B. 8
C. 10
D. 12
E. 18

ankur2710 · Answer

IMO, 12 Days

Lets say Work for making a Bench (B) = x
So, Work for making a table (T) = 3x

Assuming Work per worker per day remains constant

So,
 
(36B + 5T)/12/6 = (61B+8T)/10/D, where D is what we are looking for.

Solving this, 
51x / 72 = 85x / 10D
D=12

paddyboy · Answer

12 days.

6 workers can make 36 benches and 5 tables in 12 days i.e. 51 benches in 12 days
Or 2 workers can make 17 benches in 12 days

61 benches and 8 tables would be equivalent to 85 (17 x 5) benches. Therefore 10 (2 x 5) workers would be able to complete the work in the same time i.e. 12 days.

KarishmaB · Answer

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

GMATGuruNY · Answer

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 
 12 days

prabsahi06 · Answer

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.

GMATGuruNY · Answer

\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

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

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