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# The proportion of annual expense on food in a household remains

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Math Expert
Joined: 02 Aug 2009
Posts: 8336
The proportion of annual expense on food in a household remains  [#permalink]

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06 Dec 2017, 10:36
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Difficulty:

35% (medium)

Question Stats:

62% (01:24) correct 38% (01:08) wrong based on 109 sessions

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The proportion of annual expense on food in a household remains constant even after the annual expense on food increases by 20%. What would be the increase in Total annual expense?

(A) 0%
(B) 10%
(C) 20%
(D) 25%
(E) Cannot be determined

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Re: The proportion of annual expense on food in a household remains  [#permalink]

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06 Dec 2017, 10:43
I think its E

Bcoz answer depends on how many other proportions are there in the household.

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Re: The proportion of annual expense on food in a household remains  [#permalink]

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06 Dec 2017, 12:11
chetan2u wrote:
The proportion of annual expense on food in a household remains constant even after the annual expense on food increases by 20%. What would be the increase in Total annual expense?

(A) 0%
(B) 10%
(C) 20%
(D) 25%
(E) Cannot be determined

Let the proportion of expense on food to the total expense be x:y

The expense on food increases by 20%, making the expense on food 1.2x
Since this proportion has to remain constant, the total expense must become 1.2y(a 20% increase) (Option C)
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Re: The proportion of annual expense on food in a household remains  [#permalink]

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17 Dec 2018, 09:40
chetan2u wrote:
The proportion of annual expense on food in a household remains constant even after the annual expense on food increases by 20%. What would be the increase in Total annual expense?

(A) 0%
(B) 10%
(C) 20%
(D) 25%
(E) Cannot be determined

solution:

lets assume the annual expense to be 100, then assume the food expense be 20.
now it says that after the increase on food expense by 20% the proportion remains the same.

then
let the new household expense be x

20/100= (20*120/100)/x

x=120.

that means the new total expense is also increased by 20%.

So, C is the correct solution.
Re: The proportion of annual expense on food in a household remains   [#permalink] 17 Dec 2018, 09:40
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