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

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

Answer B

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$

Got it!

Thanks pandeyashwin

Bunuel please let me know where I am wrong.

My thinking: 20% increase in prices result in 4 gallons lesser oil.
=> $600 of 20% = $120 would be cost of 4 gallons
cost on 1 gallon = 120/4 = $30

increase in cost - 20% of $30 = $6

600 price -> 600*1.20 = 720.

+120 = -4L

+30 = -1L

Therefore new price per litre is $30. 30*x = 720.. x = 24...

Therefore original $600/$30 = 20 cans.. 20 x 1.20 = 25 cans.. 600/25 = $25

$30 - $25 = $5

Solution:

Before proceeding to solve, please know that for two quantities that are inversely proportional to each other if there is an increase of x/y in one of the term, there is a decrease of x/(x+y) in the other.
Since price and consumption are inversely proportional for a constant expenditure of $600, an increase of 20% or 1/5 as a fraction (thus x=1 and y=5) will cause a decrease of x/(x +y) in the consumption which is 1/(1+5) or 1/6 as a fraction.

This 1/6 as reduction is equivalent to 4 gallons => 1/6 =4 or 1 representing the initial consumption is 6*4=24 gallons.

So,he earlier consumed 24 gallons at 600$ and hence the price/gallon 600/24 = 25$

Now he consumes 24-4=20 gallons at 600$ and hence the price/gallon is 600/20=30$

Thus dollar increase in the price of oil per gallon = 30-25 =5$ (option b)

PS-(If its a decrease of x/y then corresponding increase in the other variable is x/|(y-x)|)

Happy Studying
Devmitra Sen
GMAT SME

The price and the quantity are INVERSELY PROPORTIONAL.
If the price is multiplied by a factor of 2/1, then 1/2 the quantity can be purchased.
If the price is multiplied by a factor of 2/3, then 3/2 the quantity can be purchased.
If the price is multiplied by a factor of 3/4, then 4/3 the quantity can be purchased.

Since the price increases by 20%, we get:
\(\frac{new-price}{old-price} = \frac{120}{100} = \frac{6}{5}\)
Thus:
At the higher price, 5/6 of the original quantity can be purchased, implying a decrease of 1/6.

Since 1/6 of the original quantity is equal to a decrease of 4 gallons, we get:
\(\frac{1}{6}Q = 4\)
\(Q = 24\)

Thus:
Original price \(= \frac{expenditure}{original-quantity} = \frac{600}{24}= 25\)
20% price increase = 20% of $25 = $5

One way of solving it is in the photograph attached along with the post.

Let x be price of one gallon oil and y number of gallons.


xy = 600

1.2x(y-4) = 600.

Therefore

xy= 1.2x(y-4)

xy = 1.2xy - 4.8x

xy-1.2xy = -4.8x

-0.2xy = -4.8x

But xy = 600
4.8x = 120

x = 120/4.8

x = 25.
20% increase equals 30

Price increase= 30-25 = 5.

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