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# In a village, the production of food grains increased by 40% and the p

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Math Expert
Joined: 02 Sep 2009
Posts: 64068
In a village, the production of food grains increased by 40% and the p  [#permalink]

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02 Apr 2020, 10:48
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Difficulty:

45% (medium)

Question Stats:

61% (02:47) correct 39% (01:39) wrong based on 22 sessions

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In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to

A. 16
B. 13
C. 10
D. 7
E. 6

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Intern
Joined: 31 Jan 2020
Posts: 2
In a village, the production of food grains increased by 40% and the p  [#permalink]

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02 Apr 2020, 11:11
Per capita production(PCP)=Total production(TP)/population(P)
For convenience, assume TP=10000 and P=100 then PCP would be 100.
Now, TP increased by 40%(new TP=14000) and PCP by only 27%(new PCP=127), so there must be an increase in population.
Put the same in PCP equation:

127=14000/New population
New Population=> 14000/127 =110.23
Old population=100, New Population=110~(approx.)
10% increase in population. So, the answer is C 10%.
Intern
Joined: 21 Sep 2012
Posts: 11
Location: United States
Concentration: Operations, General Management
GPA: 3.5
In a village, the production of food grains increased by 40% and the p  [#permalink]

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02 Apr 2020, 11:15
Say,

F1 = 100
F2 = 140 (after 40% increase)

F1/H1 = 100/n
F2/H2 = 140/n+x

127% of 100/n = 140/(n+x)
solving you get :-
x=13n/127
so rounded x=n/10

Now increase = (n/(10*n))*100 = 10%

OA - C

Bunuel wrote:
In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to

A. 16
B. 13
C. 10
D. 7
E. 6
Director
Joined: 25 Jul 2018
Posts: 712
Re: In a village, the production of food grains increased by 40% and the p  [#permalink]

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02 Apr 2020, 11:24
Let’s say that :
—> total production —T
—> population —p
—> production per capita —c
———————————————
T = pc
1.4 T = (p+a)* 1.27c
—> 1.4 T = 1.27pc + 1.27a
1.4 pc = 1.27 pc + 1.27 ac
0.13 pc = 1.27 ac
—> a =( 0.13/1.27)p = 0.1p
That means population of the village increased by 10 percent

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Re: In a village, the production of food grains increased by 40% and the p   [#permalink] 02 Apr 2020, 11:24