The juice stall at the circus stocked just 2 brands of orang

Question

The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to m% of stall’s revenue and accounted for n% of sales of juice tetra packs. Which of the following expresses m in terms of n?

(A) 100n/(150 – n)
(B) 200n/(250-n)
(C) 200n/(300-n)
(D) 250n/(400-n)
(E) 300n/(500-n)

(A) 100n/(150 – n)
(B) 200n/(250-n)
(C) 200n/(300-n)
(D) 250n/(400-n)
(E) 300n/(500-n)

Bunuel · Answer

"Stolen" OG question: Discussed here: last-sunday-a-certain-store-sold-copies-of-newspaper-a-for-101739.html

SVaidyaraman · Answer

1. Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold.

Total revenue= Revenue due to A + Revenue due to B

= (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B)

= n *1 + (100-n) *1.5 
= n + (150-1.5n) --- (1)

2. But we know, revenue due to A = m%. of the total revenue --- (2)
3. To express m in terms of n we need to relate (1) and (2)
4. m% = n / ( n + (150-1.5n))
or m= 100n / 150-0.5n = 200n/(300-n)

jlgdr · Answer

I like to use a combination of Smart Numbers and Backsolving to solve these questions. As Bunuel pointed out very similar to one found in the OG

So if I say total units = 100
and then n = 50%

So a =50%

I will get that 50/50+75=2/5

So m= 2/5=40%

So my target is 40 and my input variable is 50

I always like starting with C

200*50 / 5*250 = 40

Jackpot!

C it is

Hope it helps
Cheers!
J

ScottTargetTestPrep · Answer

Let’s let p = the total number of juice tetra packs. Since brand A accounts for n% (or n/100) of the sales of the juice tetra packs, brand B accounts for (100-n)% (or (100 - n)/100) of the the sales of the juice tetra packs. Therefore, we have:

Sales of Brand A juice / total sales = fraction of stall revenue from Brand A sales

/   = m/100

(n/100)/  = m/100

n/  = m/100

100n/  = m

200n/  = m

Answer: C

fskilnik · Answer

Let´s explore an  AGGRESSIVE PARTICULAR CASE :

n = 100  : in this case, only brand A was sold, hence all revenue came from brand A and our  FOCUS  will be (the  TARGET ) m =100 (of course)!

\left. \begin{gathered}
 \left( A ight)\,\,\,\frac{{{{10}^4}}}{{50}} 
e 100 \hfill \
 \left( B ight)\,\,\frac{{2 \cdot {{10}^4}}}{{150}} 
e 100 \hfill \
 \left( C ight)\,\,\frac{{2 \cdot {{10}^4}}}{{200}} = 100\,\,\,\,\, \hfill \
 \left( D ight)\,\,\frac{{25 \cdot {{10}^3}}}{{300}} 
e 100 \hfill \
 \left( E ight)\,\,\frac{{3 \cdot {{10}^4}}}{{400}} 
e 100 \hfill \ 
\end{gathered} ight\}\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{	ext{only}}\,\,{	ext{survivor}}\,{	ext{!}}} \,\,\,\,\,\,\,\left( C ight)

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

bumpbot · Answer

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The juice stall at the circus stocked just 2 brands of orang

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