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In the year 2001, a man spends 40% of his total

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In the year 2001, a man spends 40% of his total [#permalink]

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New post 25 Apr 2017, 04:19
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

61% (02:36) correct 39% (02:32) wrong based on 66 sessions

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In the year 2001, a man spends 40% of his total income on food. In 2002 his income increases by 40% and his expenditure on food increases by 50% with respect to 2001. In 2003 his income increases by another 25% based on 2002 and his expenditure on food increase by 16.66% based on the expenditure on food in 2001. What percent of his total income in 2003 is his expenditure on food ?

A. 66.67%
B. 50%
C. 37.5%
D. 33.33%
E. 26.67%

Posting after making a search. The solution I have is complicated hence could not figure it out. Kindly explain with simple approach. Thanks in advance!
[Reveal] Spoiler: OA

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Re: In the year 2001, a man spends 40% of his total [#permalink]

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New post 25 Apr 2017, 04:32
Solution: 26.67%(Option E)
Let income be i, expenditure on food be e
Year 2001
i=200,e=80(40% on food)
Year 2002
i=280(increase of 40%)
e=120(50% increase over 2001)
Year 2003
i=350(another 25% over 2002)
e=560/6(increase of 16.67 or 1/6th on food expenditure in 2001)

Percentage = (560/(6*350))*100 = 26.67%


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Re: In the year 2001, a man spends 40% of his total [#permalink]

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New post 13 May 2017, 05:15
I didn't get it could any one explain ?
please

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Re: In the year 2001, a man spends 40% of his total [#permalink]

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New post 20 Sep 2017, 10:32
pushpitkc wrote:
Solution: 26.67%(Option E)
Let income be i, expenditure on food be e
Year 2001
i=200,e=80(40% on food)
Year 2002
i=280(increase of 40%)
e=120(50% increase over 2001)
Year 2003
i=350(another 25% over 2002)
e=560/6(increase of 16.67 or 1/6th on food expenditure in 2001)

Percentage = (560/(6*350))*100 = 26.67%


"e=560/6(increase of 16.67 or 1/6th on food expenditure in 2001)" this part seems wrong. 560/6 ~ 93.33. But the question says food expenditure increases by 16.67% over 2001. So it should come to ~123.33 and answer should be ~37%. Correct me if I am wrong.

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In the year 2001, a man spends 40% of his total [#permalink]

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New post 22 Sep 2017, 21:46
vinay888 wrote:
pushpitkc wrote:
Solution: 26.67%(Option E)
Let income be i, expenditure on food be e
Year 2001
i=200,e=80(40% on food)
Year 2002
i=280(increase of 40%)
e=120(50% increase over 2001)
Year 2003
i=350(another 25% over 2002)
e=560/6(increase of 16.67 or 1/6th on food expenditure in 2001)

Percentage = (560/(6*350))*100 = 26.67%


"e=560/6(increase of 16.67 or 1/6th on food expenditure in 2001)" this part seems wrong. 560/6 ~ 93.33. But the question says food expenditure increases by 16.67% over 2001. So it should come to ~123.33 and answer should be ~37%. Correct me if I am wrong.


No, he's right. Let me explain

2001
i = 100
e = 40

2002
i = Based on 2001 = 100+0.4*100= 140
e = Based on 2001 = 40+0.5*40 = 60

2003
i = Based on 2002 = 140+0.25*140 = 175
e = Based on 2001 = 40+(40/6 or 0.1667*40) = 280/6 or 46.67

-> (280/6 / 175)*100 = 26%

The question says income in 2003 "increases by another" 25% based on 2002, but expenditure food in 2003 "increases" by 16,67 % based on 2001, which you have to start over with 40, not 60.

So, the answer is (E)

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In the year 2001, a man spends 40% of his total   [#permalink] 22 Sep 2017, 21:46
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