If the productivity of a brigade increases by 10% with the addition of

Question

If the productivity of a brigade increases by 10% with the addition of each worker, which of the following is the ratio of the productivity of a 12-person brigade to a 10-person brigade?

A. 0.21
B. 0.82
C. 1.20
D. 1.21
E. 1.44

KarishmaB · Accepted Answer

In percentages, you can assume a value of 100. It simplifies the thought process.

If you increase the brigade by 1 worker, productivity grows by 10%. So say initial productivity is 100. If one more worker joins, productivity will be 110. If one more joins it will be 121 etc. 
Ratio of productivity of 12 person to 10 person must be 121/100 = 1.21 (whenever there is a difference of 2 in the number of people, the ratio of productivity will be 1.21 assuming positive number of people)

Also, this is a successive percentage increase so you can use the formula: a + b + ab/100 = 10 + 10 + 10*10/100 = 21% increase.
Hence the required ratio is 121/100 = 1.21

sondenso · Answer

D, 
productivity of a 10-men brigade assumed is 10
when added 1 man, it is increasing by 10*1.1 =11
when added 1 more, it s increasing by 11*1.1 =12.1= productivity of a 12-men brigade
so, the ratio=12.1/10 =1.21

Stiv · Answer

This is the question from GMATClub test. The explanation from the solution of the question is excellent, but I want to know is there more than one way to solve this question.

On the GMATClub test the explanation is next:
B = 10-men brigade
p = increase in the productivity = 10%

Solution: B x p = B x 1.1 = 1.1B -------> the productivity of 11 men brigade
 1.1B x p = 1.1B x 1.1 = 1.21B -----> the productivity of 12 men brigade

The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.21B/B = 1.21

ScottTargetTestPrep · Answer

We can let a 10-person brigade’s productivity be 100; thus, a 11-person brigade’s productivity will be 100 x 1.1 = 110, and a 12-person brigade’s productivity will be 110 x 1.1 = 121. Therefore, the ratio is 121/100 = 1.21.

Answer: D

Bunuel · Answer

If the productivity of a brigade increases by 10% with the addition of each worker, which of the following is the ratio of the productivity of a 12-person brigade to a 10-person brigade?

A. 0.21
B. 0.82
C. 1.20
D. 1.21
E. 1.44

Let's assume the productivity of a 10-person brigade is 1. Then, the productivity of a 12-person brigade would be  1.1*1.1 = 1.21 .
 
Therefore, the desired ratio is  \frac{1.21}{1} = 1.21 .

Answer: D

eaqueest · Answer

I work as Production engineer, this approach came to my mind.

Initially, I have 1 person who can produce one product.

Productivity of adding one person, makes 1.1 product.

Productivity of adding 10 persons, makes (1.1)^10 products.
Productivity of adding 12 persons, makes (1.1)^12 products

Ratio of (1.1)^12 and (1.1)^10, leaves (1.1)^2 = 1.21

If the productivity of a brigade increases by 10% with the addition of

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