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profit and loss

This topic has 2 expert replies and 2 member replies

profit and loss

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By selling oranges at $p for 1.66 dozen , a vendor makes a profit of r%. If he had bought them at the rate of q for $12, what does 5pq-12r equal ?
A 12
B 120
C 240
D 1200
E 2400

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1.66 Dozen = 1.66 * 12
Pp = 19.92 Oranges.
$$\Pr ofit\ of\ r\text{}\%\ =\ \frac{1}{100}$$
5pq , rate of q = %12
5pq - 12r = ??

$$5\left(19.92\ \cdot\ 12\ \right)\ \frac{\left(-12r\right)}{100}\ =\ x$$
$$5\ \cdot\ 239.04\ \frac{-12r}{100}\ =\ x$$
$$\frac{\left(1195.2\ -\ 12\right)r}{100}=\ x$$
$$\ x\ =\ \frac{183.2}{100}r$$
x = 11.832
x = 12
Option A is the correct answer.

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vaibhav101 wrote:
By selling oranges at $p for 1.66 dozen , a vendor makes a profit of r%. If he had bought them at the rate of q for $12, what does 5pq-12r equal ?
A 12
B 120
C 240
D 1200
E 2400
1.66 dozen = (5/3) x 12 = 20 oranges. Pick a total price P so that price per orange is nice, say $20, so $1 per orange.

Pick a cost per orange that generates a nice profit, say 100%. A cost per orange of $.50 should work, but let's check:

r% = 100x($1-$.50)/$0.50 = 100 x 1 = 100

Since he paid $12 for q oranges, the cost per orange is $12/q = $0.50. Therefore, q=24 oranges

Substitute these values into 5pq-12r = (5)(20)(24) - (12)(100) = 2400-1200 = D, 1200

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vaibhav101 wrote:
By selling oranges at $p for 1.66 dozen , a vendor makes a profit of r%. If he had bought them at the rate of q for $12, what does 5pq-12r equal ?
A 12
B 120
C 240
D 1200
E 2400
Since 1.66 dozen = 5/3 x 12 = 20, the vender sells 20 oranges for $p and he bought them at a rate of q oranges for $12. So he sells them for p/20 dollars each and bought them for 12/q dollar each. Since the the profit is r%, we have:

p/20 - 12/q = r/100 x 12/q

p/20 - 12/q = 12r/(100q)

Multiplying the equation by 100q, we have:

5pq - 1200 = 12r

5pq - 12r = 1200

Answer: D

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Scott Woodbury-Stewart Founder and CEO

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vaibhav101 wrote:
By selling oranges at $p for 1.66 dozen , a vendor makes a profit of r%. If he had bought them at the rate of q for $12, what does 5pq-12r equal ?
A 12
B 120
C 240
D 1200
E 2400
Let r=0, implying that no profit is made and that the oranges are sold at cost.

Let q=12, implying that the cost for 12 oranges is $12, with the result that the cost per orange = $1.
1.66 dozen = (5/3)(12) = 20 oranges.
Since the cost for 20 oranges = $20, p=20.
Thus:
5pq - 12r = (5*20*12) - (12*0) = 1200.

The correct answer is D.

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