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A retailer adds freely available water to an orange concentrate

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A retailer adds freely available water to an orange concentrate  [#permalink]

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New post 01 Mar 2018, 12:38
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E

Difficulty:

  65% (hard)

Question Stats:

55% (02:11) correct 45% (02:12) wrong based on 83 sessions

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A retailer adds freely available water to an orange concentrate, costing $50 per liter, to prepare an orange drink. He sells the drink at $30 per liter and earns 50% profit on his investment. How many liters of water does he add to each liter of the orange concentrate?

A. 0.5
B. 0.60
C. 0.67
D. 1
E. 1.5

Source: Experts Global

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A retailer adds freely available water to an orange concentrate  [#permalink]

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New post 01 Mar 2018, 15:30
1
pushpitkc wrote:
A retailer adds freely available water to an orange concentrate, costing $50 per liter, to prepare an orange drink. He sells the drink at $30 per liter and earns 50% profit on his investment. How many liters of water does he add to each liter of the orange concentrate?

A. 0.5
B. 0.60
C. 0.67
D. 1
E. 1.5

Source: Experts Global



sale price=1.5*$50=$75
$75/$30=2.5 liters sold
2.5 liters-1 liter oc=1.5 liters water added
E
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Re: A retailer adds freely available water to an orange concentrate  [#permalink]

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New post 01 Mar 2018, 17:11
pushpitkc wrote:
A retailer adds freely available water to an orange concentrate, costing $50 per liter, to prepare an orange drink. He sells the drink at $30 per liter and earns 50% profit on his investment. How many liters of water does he add to each liter of the orange concentrate?

A. 0.5
B. 0.60
C. 0.67
D. 1
E. 1.5

Source: Experts Global

Find cost from revenue, then volume from cost.

• Find cost from revenue
Suppose he sells 10 liters for $30 per liter.
(10 * $30) = $300 Total revenue

That revenue earns him 50% profit on his investment
Revenue = 150% Cost = 1.5(Cost)
1.5(Cost) = $300
Cost =\(\frac{$300}{1.5}\)=$200

• Liters of OJ used in mix sold?

Cost = $200
Cost per liter of OJ = $50
Cost per liter of water = $0

\(\frac{TotalCost}{CostPerLiter} =\) # of liters of OJ

For 10L of mix he used
\(\frac{$200}{$50}=4\) liters of OJ concentrate

• Liters of water used in mix?
(10L mix - 4L OJ) = 6L of water used

• Liters of water added to liter of OJ to make mix?
Volume ratio is

\(\frac{Water}{OJ}=\frac{6}{4}=\frac{3}{2}=\frac{1.5}{1}=1.5\) L of water per L of OJ

Answer E

Alternatively, ONE liter sold.
Revenue = 1.5C
$30 = 1.5C

Cost:\(\frac{$30}{1.5} = $20\)

Volume of $20 worth of OJ at \(\frac{$50}{L}\)
\(\frac{$20}{$50}=\frac{2}{5}\) L of OJ

1 L mix sold. \(\frac{2}{5}\) L is OJ
1L - \(\frac{2}{5}\) L = \(\frac{3}{5}\) L of water

\(\frac{Water}{OJ}=\frac{\frac{3}{5}}{\frac{2}{5}}=\frac{3}{2}=1.5\) liters of water added per L of OJ

Answer E
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Re: A retailer adds freely available water to an orange concentrate  [#permalink]

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New post 03 Mar 2018, 00:00
First, we need to find the final concentration of orange concentrate in the drink. Which is 40% ( ($30-$c)/$c=0.5)-----> c= $20 ----> we can buy 0.4L of the concentrate with $20). The question now boils down to how much water is to be added to a 100% concentrate to make it a 40% concentrate. This is 1/(1+W) = 0.4 ----> w =1.5L.

pushpitkc wrote:
A retailer adds freely available water to an orange concentrate, costing $50 per liter, to prepare an orange drink. He sells the drink at $30 per liter and earns 50% profit on his investment. How many liters of water does he add to each liter of the orange concentrate?

A. 0.5
B. 0.60
C. 0.67
D. 1
E. 1.5

Source: Experts Global
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Joined: 29 Mar 2017
Posts: 19
Location: India
GMAT 1: 720 Q49 V39
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Re: A retailer adds freely available water to an orange concentrate  [#permalink]

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New post 03 Mar 2018, 00:54
we can use the allegation general formula here..
Quantity of cheaper/quantity of derar=(price of dearer-price mean price)/
(mean price-price of cheaper)
here mean price = 20(as sp is 30 and profit is 50%)
hence, Qty of water/qty of orange concentrate=(50-20)/(20-0)=30/20-3/2
now, since orang concentrate is 1l, qty of water = 3/2=1.5L.
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Re: A retailer adds freely available water to an orange concentrate &nbs [#permalink] 03 Mar 2018, 00:54
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