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The price of sugar is increased by 7%. By how much percent

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The price of sugar is increased by 7%. By how much percent  [#permalink]

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New post 03 Jul 2013, 22:17
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A
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Question Stats:

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The price of sugar is increased by 7%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?

A. (700/107) %
B. (107/100) %
C. (100/107)%
D. (7/100)%
E. (100/700)%
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Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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New post 03 Jul 2013, 22:47
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DarkKnight06 wrote:
The price of sugar is increased by 7%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?

A. (700/107) %
B. (107/100) %
C. (100/107)%
D. (7/100)%
E. (100/700)%


Old price = $100 (assume);
Old consumption = 1 kg (assume).

New price = $107.

We want the spendings to remain at $100.
(New consumption)*107 = 100 --> (New consumption) = 100/107 kg.

Percent decrease = Change/Original *100 = (1 - 100/107)/1*100 = 700/107%.

Answer: A.

Else you can notice that the decrease in consumption must be very close to 7% (a bit less) and taking this into account only A makes sense.
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Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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New post 17 Oct 2014, 19:49
Bunuel wrote:
DarkKnight06 wrote:
The price of sugar is increased by 7%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?

A. (700/107) %
B. (107/100) %
C. (100/107)%
D. (7/100)%
E. (100/700)%


Old price = $100 (assume);
Old consumption = 1 kg (assume).

New price = $107.

We want the spendings to remain at $100.
(New consumption)*107 = 100 --> (New consumption) = 100/107 kg.

Percent decrease = Change/Original *100 = (1 - 100/107)/1*100 = 700/107%.

Answer: A.

Else you can notice that the decrease in consumption must be very close to 7% (a bit less) and taking this into account only A makes sense.


Hi Bunuel,

Is this approach correct:

Old price: P
Old consumption: C
New Price: 107/100P
New consumption: C* (1-x) in which x is the percentage of change
PC = 107/100P* C *(1-x) => 107/100*(1-x) = 1
1-x=100/107
x= 1-100/107 = 7/107
x% = 700/107%
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Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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New post 12 Dec 2015, 11:44
did half the work, and marked 100/107 ..eh..dumb me..
should have read the question more attentively..A is the correct answer.
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Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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New post 15 Jan 2016, 23:06
price and consumption are reversely proportional if spending is the same.

if price increases 107/100 times, consumption decreases 107/100 times, so final consumption becomes 100/107 of initial

107/107-100/107=7/107 => (7/107)*100/1=700/107

A
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Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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New post 16 Jan 2016, 00:51
DarkKnight06 wrote:
The price of sugar is increased by 7%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?

A. (700/107) %
B. (107/100) %
C. (100/107)%
D. (7/100)%
E. (100/700)%


assume she got 100 kg for 100 rs
after increase in price she will get 100 kg for 107 rs
she has to spend 100 rs only, so at new price she gets (100*100/107) for 100 rs
% change = 100 - (100*100/107) = 700/107 %
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Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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New post 17 Jan 2016, 21:09
Hi All,

The answer choices to this question are written in such a way that you can avoid most of the 'math work' and answer this question with a bit of logic.

We're told that the price of sugar is increased by 7%. We're asked by what percent a home maker should reduce her consumption of sugar to have no extra expenditure. In real basic terms, we need to reduct the amount of sugar by a certain percent so that no extra money is spent.

Since the price of sugar increased by 7%, we'll have to decrease the consumption by a value that's relatively close to 7% (but NOT 7% exactly). Now look at the answers and really think about what they 'translate' into:

A. (700/107) % = a little less than 7%
B. (107/100) % = a little more than 1%
C. (100/107)% = a little less than 1%
D. (7/100)% = less than 1/10 of 1%
E. (100/700)% = 1/7 of 1%

There's only one answer choice that makes any sense given the situation described...

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Re: The price of sugar is increased by 7%. By how much percent  [#permalink]

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New post 18 Jun 2018, 01:15
DarkKnight06 wrote:
The price of sugar is increased by 7%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?

A. (700/107) %
B. (107/100) %
C. (100/107)%
D. (7/100)%
E. (100/700)%



Easy enough!

Just remember the formula -

" If the price of an item goes up/down by x%, then the quantity consumed should be increased/reduced by (100x/(100+/-x))% so that the total expenditure remains the same."


That would be -
(7*100/100+7)%
= (700/107)%
Option A
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The price of sugar is increased by 7%. By how much percent  [#permalink]

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New post 29 Aug 2018, 05:56
1
This can be solved with substituting numbers, (credits go to @rahul2013)
100usd per 1kg. I consume 10kg, so spend 1000 usd. Now, the price is 107, so 1000 (my total budget)/107=9.35kg now I can consume. 10kg-9.35=0.65*100%=6.35% or A
The price of sugar is increased by 7%. By how much percent &nbs [#permalink] 29 Aug 2018, 05:56
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