When Brenda took over a restaurant, 20% of its revenue came

Question

When Brenda took over a restaurant, 20% of its revenue came from breakfast customers. After she introduced new breakfast items, revenue from breakfast customers increased by 60% and now accounts for 25% of the restaurant’s total revenue.

By what percent did revenue from non-breakfast items increase ?

A. 15%
B. 16%
C. 20%
D. 25%
E. 60%

By what percent did revenue from non-breakfast items increase ?

A. 15%
B. 16%
C. 20%
D. 25%
E. 60%

GraemeGmatPanda · Answer

We define variables and choose a convenient base for total revenue to keep calculations simple.
 R_0 = 100 	ext{ (initial total revenue, chosen for convenience)} 
 B_0 = 	ext{initial breakfast revenue} 
 N_0 = 	ext{initial non-breakfast revenue}

We translate the statement that 20% of initial revenue came from breakfast customers into an equation.
 B_0 = 0.20 	imes R_0

We translate the changes: breakfast revenue increases by 60%, and after the change breakfast revenue is 25% of the new total revenue.
 B_1 = 1.60 	imes B_0 
 B_1 = 0.25 	imes R_1

We express non-breakfast revenue before and after as total minus breakfast revenue.
 N_0 = R_0 - B_0 
 N_1 = R_1 - B_1

We substitute the expressions for  B_1  and  B_0  to solve for  R_1  in terms of  R_0 .
 1.60 	imes B_0 = 0.25 	imes R_1 
 1.60 	imes 0.20 	imes R_0 = 0.25 	imes R_1 
 0.32 	imes R_0 = 0.25 	imes R_1 
 R_1 = \frac{0.32}{0.25} 	imes R_0 = 1.28 	imes R_0

We compute non-breakfast revenues before and after using the relation for  R_1 , then compute the percent increase for non-breakfast revenue.
 N_0 = 0.80 	imes R_0 
 N_1 = R_1 - B_1 = 1.28 	imes R_0 - 0.32 	imes R_0 = 0.96 	imes R_0 
 	ext{Percent increase} = \frac{N_1 - N_0}{N_0} 	imes 100\% = \frac{0.96R_0 - 0.80R_0}{0.80R_0} 	imes 100\% 
 = \frac{0.16}{0.80} 	imes 100\% = 0.20 	imes 100\% = 20\%

Answer C

Hope this helps! 
ʕ•ᴥ•ʔ

harjas2222 · Answer

Let the total income before percent change be=$1000

now 20/100*1000= 200 dollars earned by Breakfast, while 800 by non breakfast

Now 200 (1.6) = 320

which (25/100) * x = 320, 
cut
(1/4)*x=320, x= 320*4= 1280

remaing income will be non breakfast= 1280-320=960

960-800/100 * x= 20%

egmat · Answer

Let's pick a nice round number for the original total revenue. Say the restaurant originally made  100  dollars total.

Step 1:  Find original breakfast and non-breakfast revenue.
- Breakfast was  20%  of  100  =  20  dollars
- Non-breakfast was the rest =  100 - 20 = 80  dollars

Step 2:  Find new breakfast revenue.
- Breakfast revenue increased by  60% 
- New breakfast revenue =  20 + 60% of 20 = 20 + 12 = 32  dollars

Step 3:  Find the new total revenue.
- We're told breakfast NOW accounts for  25%  of the new total revenue
- So  32  =  25%  of New Total
- New Total =  32 / 0.25 = 128  dollars

Step 4:  Find new non-breakfast revenue.
- New non-breakfast = New Total - New Breakfast =  128 - 32 = 96  dollars

Step 5:  Find the  percent increase  in non-breakfast revenue.
- Non-breakfast went from  80  to  96 
- Increase =  96 - 80 = 16 
- Percent increase =  16 / 80 × 100 = 20%

Answer: C (20%)

A common mistake  here is to confuse the  16  dollar increase with  16%  (choice B). But remember,  percent increase  is always calculated relative to the ORIGINAL value ( 80 ), not relative to the total ( 100 ).  16  out of  80  is  20% , not  16% .

Stella5200 · Answer

was a little diff to squeeze into 2 mins but I was able to do It:

We need to find Breakfast a Non Breakfast.

Breakfast org: B was 20% of Revenue
So org Revenue was 5B 
and Non breakfast was 4B of it

New Breakfast grew to 1.6 x B (B is org breakfast)

This is 25% so total revenue 4 x 1.6 B = 6.4

No breakfast portion is 6.4 - 1.6 =4.8 B,

So non breakfast chnage is 4.8/4 -1 =0.2 12/10-1 =20%

I find straight algebra to be too cumbersome here.

kevincan · Answer

..........B not B. Total
First 20 ...80 ......100
Then 32 ............ 128
Final not B 96

96/80 =1.2

Adit_ · Answer

There are multiple variables working here.
There is the first case before the revenue increase and then the second case which is after the revenue increase.

Initially we have lets say 20 out of 100 from breakfast.
Then increase by 60% = 32.
Now this 32 became 1/4th of new increased revenue = 128  
Thus non breakfast in this new segment would give us 128-32 = 96.

Old non breakfast revenue = 100-20 = 80.
Thus increase from 80 to 96 is increase percent of 20%.

Answer:  Option C

When Brenda took over a restaurant, 20% of its revenue came

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When Brenda took over a restaurant, 20% of its revenue came

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