Question

The production of a company for three successive years has increased by 10%, 30%, 90% respectively. What is average annual increase production
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Answer 1

Average annual increase in production = 30%

Step-by-step explanation:

Given: The production of a company for three successive years has increased by 10%, 30%, 90% respectively.

Find: What is average annual increase in production

Solution:  

The production of a company for three successive years has increased by 10%, 30%, 90% respectively. To find the average annual increase of three percentage values, we have to find the cube root of the product of the three values.

Average = (10 * 30 * 90)^(1/3)

       = 27000^(1/3)

       = 30

Average annual increase in production = 30%

Answer 2

Given :  The production of a company for three successive years has increased by 10%, 30%, 90% respectively

To find : Average annual increase production

Solution:

The production of a company for three successive years has increased by 10%, 30%, 90% respectively

Let say initial production = P

production after 1 year - P(1 + 10/100) = 1.1P

Production after 2nd year = 1.1P(1 + 30/100)  =  1.1P * 1.3  = 1.43P

Production after 3rd  year = 1.43P(1 + 90/100)  =  1.43P * 1.9  = 2.717P

average annual increase production for  compounded  = R

then P ( 1 + R/100)³ = 2.717P

=> 1 + R/100 = 1.395

=> R = 39.5 %

average annual increase production  = 39.5 %

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if average is calculated without compounding then

100 * (1.717)/3 =  57.23%

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