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Due to a sudden 20% increase in price, one is now able to buy 4 gallon

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Due to a sudden 20% increase in price, one is now able to buy 4 gallon  [#permalink]

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17 Oct 2017, 05:28
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Difficulty:

65% (hard)

Question Stats:

61% (02:33) correct 39% (02:38) wrong based on 87 sessions

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Due to a sudden 20% increase in price, one is now able to buy 4 gallons lesser oil than earlier on the same expenditure of
$600. What is the dollar increase in the price of oil per gallon? A.$2
B. $5 C.$10
D. $20 E.$25

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Re: Due to a sudden 20% increase in price, one is now able to buy 4 gallon  [#permalink]

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19 Oct 2017, 10:16
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1
nkmungila wrote:
Due to a sudden 20% increase in price, one is now able to buy 4 gallons lesser oil than earlier on the same expenditure of
$600. What is the dollar increase in the price of oil per gallon? A.$2
B. $5 C.$10
D. $20 E.$25

We can let the original number of gallons of oil = n and the original price = p; thus:

np = 600

and

(1.2p)(n - 4) = 600

1.2np - 4.8p = 600

Substituting 600 for np in the above equation, we have:

1.2(600) - 4.8p = 600

720 - 4.8p = 600

120 = 4.8p

25 = p

The old price was 25, and the new price is 20% more: 25 x 1.2 = 30. Thus, the increase in price is 5 dollars.

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Re: Due to a sudden 20% increase in price, one is now able to buy 4 gallon  [#permalink]

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20 Oct 2018, 13:12
1
castiel wrote:
Can we solve this using a logical approach??

Apart from algebra you could solve it using percentage.

Initial amount = 100
Now price increased by 20% = 120
Since the price increased , you need to decrease consumption by 20/120 * 100 = 16.67% or 1/6 to keep your expenditure the same.

This 16.67% decrease = 4 units of gasoline
Therefore , 100% = 24 units of gasoline
Initial quality = 24 units ; Initial price = 600/24 = 25$Final quantity = 20 units ; Final Price = 600/20 = 30$

Increase = 5$Senior SC Moderator Joined: 22 May 2016 Posts: 3670 Due to a sudden 20% increase in price, one is now able to buy 4 gallon [#permalink] Show Tags 17 Oct 2017, 06:14 nkmungila wrote: Due to a sudden 20% increase in price, one is now able to buy 4 gallons lesser oil than earlier on the same expenditure of$600. What is the dollar increase in the price of oil per gallon?

A. $2 B.$5
C. $10 D.$20
E. $25 Test the answers. The equation for this one was taking too long. Backsolving was quick. (Price per gallon P) * (# of gallons Q) = Total cost Q = Total cost/price per gallon 1) Find original price from given dollar increase 2) Find original # of gallons by dividing$600 by old price per gallon

3) Find new price
= (1.2)($old), OR ($Old price + added $increase) 4) Find new # gallons. Divide 600 by new price Answer C)$10

$10 is both the dollar increase in price and a .20 increase of original price, x Original price:$10 = .2x = $$\frac{10}{.2} = 50$$

Original number of gallons:

$$\frac{600}{50PerGal} = 12$$ gallons

New price: $50 +$10 (or 1.2 * $50) =$60

New number of gallons

$$\frac{600}{60per} = 10$$ gallons

12 - 10 = 2 fewer gallons now. Too small. That means the dollar price increase is too large. To increase quantity, decrease price.

Try B) $5$5 = .2x

Original price:

$$\frac{5}{.2} = 25$$

Original quantity:

$$\frac{600}{25per} = 24$$ gallons

New price: (1.2)($25) or ($25 + $5) =$30

New quantity:

$$\frac{600}{30per} = 20$$ gallons

24 - 20 = 4 gallons. Correct

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Re: Due to a sudden 20% increase in price, one is now able to buy 4 gallon  [#permalink]

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20 Oct 2018, 12:35
Can we solve this using a logical approach??
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Re: Due to a sudden 20% increase in price, one is now able to buy 4 gallon  [#permalink]

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20 Oct 2018, 12:51
3
Let the price of gasoline be x. New Price = 1.2x

$$\frac{600}{x} - \frac{600}{1.2x} = 4$$

120 = 4.8x
x = 25
New price = 30
Increase = 5\$
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Due to a sudden 20% increase in price, one is now able to buy 4 gallon  [#permalink]

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21 Oct 2018, 01:34
Got it!

Thanks pandeyashwin
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Re: Due to a sudden 20% increase in price, one is now able to buy 4 gallon  [#permalink]

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06 Nov 2019, 01:09
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Re: Due to a sudden 20% increase in price, one is now able to buy 4 gallon   [#permalink] 06 Nov 2019, 01:09
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