BTGmoderatorLU wrote:Source: Princeton Review

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?

$$A.\ \frac{100n}{150-n}$$
$$B.\ \frac{200n}{250-n}$$
$$C.\ \frac{200n}{300-n}$$
$$D.\ \frac{250n}{400-n}$$
$$E.\ \frac{300n}{500-n}$$
The OA is C.

Say the total number of packs sold = x

Thus,
the total number of brand A packs sold = nx/100; and
the total number of brand B packs sold = x - nx/100 = (100x - nx)/100 = x(100 - n)/100

Sales revenue from the sale of brand A = nx/100 * 1 = nx/100
Sales revenue from the sale of brand B = x(100 - n)/100 * 1.5 = 3x(100 - n)/200

=> Total sales revenue from the sale of both the brands = [nx/100 + 3x(100 - n)/200]

Since it is given that brand A contributed to m% of stall's revenue, we have

[nx/100] = m% of [nx/100 + 3x(100 - n)/200]

[n/100] = m[n/100 + 3(100 - n)/200]/100; x gets cancelled
n = m[n/100 + 3(100 - n)/200]; 100 gets cancelled

200n = m(2n + 300 - 3n)

m = (200 n)/(300 - n)

The correct answer: C

Hope this helps!

-Jay
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