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% problems - Help needed

by bsharad_99 » Wed Aug 31, 2016 9:37 pm
If price decreases by 25%, by what % should consumption increase so that the expenditure does
not increase?
A) 33.33% b) 25% c) 43% d) 68% e) 65.55%

If speed increases by 33.33%, what is the percent reduction in the time taken to travel the same
distance?
A) 33.33% b) 25% c) 43% d) 68% e) 65.55%

The price of a product increased by 20% but the turnover increased by only 12%. What is the %
drop in quantity sales?
A) 33.33% b) 25% c) 43% d) 6.66% e) 65.55%
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by [email protected] » Thu Sep 01, 2016 9:57 am
Hi bsharad_99,

To start, you should list just one prompt per post - that way the conversation can stay focused on just one prompt and we can avoid the confusion of having multiple discussions on different questions in one thread.

As it stands, all 3 of these questions test the same concept and can all be solved by TESTing VALUES.

For the 1st question:

We're told that price decreases by 25%, and we're asked how much consumption needs to increase to create the same overall expenditure.

Original Price = $100
Total Consumption = $1,000
Units = 10

New Price = $75

(75)(X) = 1,000
X = 1,000/75 = 40/3 = 13.33333 units

% increase = (difference)/(original) = 3.3333/10 = 33.33%

Final Answer: A

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by Matt@VeritasPrep » Thu Sep 01, 2016 4:27 pm
bsharad_99 wrote:If price decreases by 25%, by what % should consumption increase so that the expenditure does
not increase?
A) 33.33% b) 25% c) 43% d) 68% e) 65.55%
Assuming that Price * Consumption = Expenditure (I have no idea if this is the equation, but it seems reasonable enough), we want

Old Expenditure = New Expenditure

or

Old Price * Old Consumption = New Price * New Consumption

or

p * c = (3/4)p * (x)c

Divide both sides by p * c

1 = (3/4) * x

4/3 = x

4/3 = 1 + (1/3), so we must increase by 33.33...%.
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by Matt@VeritasPrep » Thu Sep 01, 2016 4:28 pm
bsharad_99 wrote: If speed increases by 33.33%, what is the percent reduction in the time taken to travel the same
distance?
A) 33.33% b) 25% c) 43% d) 68% e) 65.55%
Distance = Rate * Time

Old Distance = New Distance, so

Old Rate * Old Time = New Rate * New Time, or

r * t = (4/3)*r * (x)*t

Divide both sides by r * t:

1 = (4/3) * x

3/4 = x

3/4 = 1 - 1/4, so time decreases by 25%.
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by Matt@VeritasPrep » Thu Sep 01, 2016 4:34 pm
bsharad_99 wrote:The price of a product increased by 20% but the turnover increased by only 12%. What is the %
drop in quantity sales?
A) 33.33% b) 25% c) 43% d) 6.66% e) 65.55%
I'd need the equation your textbook gives to relate price, turnover, and quantity. Is it Turnover = Sales/Inventory?
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