Question

What single percentage change is equivalent to a 9% increase followed by a 17% increase?

Answer 1

Given:

$9\%$ increase followed by a $17\%$ increase

To find:

Single percentage change

Solution:

Suppose a number $x$ is increased by $9\%$ followed by a $17\%$ increase

New number, $x_{1} =(1+\frac{17}{100} )(1+\frac{9}{100} )x$

$x_{1}=(1.17)(1.09)x$

$x_{1}=1.2753x$

So, the new number $x_{1}$ is $27.53\%$ more than the number $x$.

Hence,  $27.53\%$  is the single percentage change, which is equivalent to a $9\%$ increase followed by a $17\%$ increase.

Answer 2

SOLUTION :

TO DETERMINE

The single percentage change which is equivalent to a 9% increase followed by a 17% increase

EVALUATION

Let the original number be 100

It is given that the number is increased by 9 % followed by a 17% increase

So first the number is increased by 17 %

So the number becomes after increment is

$= \displaystyle \sf{ 100 \times \frac{117}{100} = 117 \: }$

Now again the number is increased by 9 %

So the number 117 becomes after an increment of 9 % is

$= \displaystyle \sf{ 117 \times \frac{109}{100} = 127.53 \: }$

So the total increment

$\sf{ = 127.53 - 100}$

$\sf{ = 27.53 }$

Hence the rate of increment in terms of single increment is

$= \displaystyle \sf{ \frac{27.53}{100} \times 100 \: \% = 27.53 \: \% }$

RESULT

The single percentage change which is equivalent to 9% increase followed by a 17% increase is 27.53 %

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