Quick way to do this one..

Let the total number of products sold be 100..

We will work with ratio of the individual revenues for Product A and Product B

\(\frac{21Q}{6(100-Q)} = \frac{T}{100-T}\)

Answer (D)

....................... Product A .................... Product B ...................

Per Piece cost...... 6 .................................. 21 ....

Sales ................. \(x - \frac{qx}{100}\) ...................... \(\frac{qx}{100}\) ....................... x (Assume-Total sales)

Total Revenue ........\(r - \frac{tr}{100}\) ..................... \(\frac{tr}{100}\) ......................... r (Assume - Total revenue)

Two equations would be setup:

\(21 * \frac{qx}{100} = \frac{tr}{100}\)

\(\frac{r}{x} = \frac{21q}{t}\) .................... (1)

\(6 * (x - \frac{qx}{100}) = r - \frac{tr}{100}\) ......... (2)

Divide the complete equation (2) by x

\(6 * (1 - \frac{q}{100}) = \frac{r}{x} - \frac{tr}{100x}\)

\(6 * (1 - \frac{q}{100}) = \frac{r}{x} * (1 - \frac{t}{100})\) .................. (3)

Placing value of \(\frac{r}{x}\) (from equation 1) in equation (3)

\(6 * (1 - \frac{q}{100}) = \frac{21q}{t} * (1 - \frac{t}{100})\)

40t = 140q - tq

\(q = \frac{40t}{140-t}\)

Answer = D

Let toatal number of product A=A and product B=B
total no. of products sold=(A+B)
total revenue= 6A+21B
As per stem
Q%(A+B)=B -------(a)
T%(6A+21B)=21B-------(b)
from(b) we get
6AT+21BT=2100B
B=6AT/(2100-21T)----(c)
from (a)
QA+QB=100B
B=QA/(100-Q)----(d)
equating (c)&(d)
2100Q-21QT=600T-6QT
Q(2100-15T)=600T
Q=600T/(2100-15T)
dividing by 15 to num. & denom.
Q=40T/(140-T)
Ans D

These questions always throw me for a loop, but picking smart numbers works best for me. Granted, this STILL took me 4 minutes:

If we buy 2 of each product, Q = 50%, and T = 42/54, or 7/9, or 77% (let's round this to 80% and save ourselves the headache).

I begin plugging in for each answer choice:

A: 1501(80) - 15(80)^2 = 1501(80) - 15(640)...no way this is 50!

B: 15(80) / 615-6(80) = ~1000 / ~200...no way this is 50!

C: 21(80) / 621-6(80) = ~1600/ ~140...no way this is 50!

D: 40(80) / 140-(80) = ~3200 / 60 ... A little over 50, THIS SEEMS PRETTY CLOSE!

E: 60(80) / 160-(80) = ~4800 / 80 ... ~60, this is definitely close too, but D is closest!

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