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# The population of city X increased by 10% in year 2013 and 15% in year

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Math Expert
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The population of city X increased by 10% in year 2013 and 15% in year  [#permalink]

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04 Jun 2020, 06:39
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Difficulty:

45% (medium)

Question Stats:

77% (01:23) correct 23% (01:41) wrong based on 31 sessions

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The population of city X increased by 10% in year 2013 and 15% in year 2014. What is the approximate population of the city at the end of year 2014, if population of the city at the starting of year 2013 was 21,000?

A. 23000

B. 25000

C. 25500

D. 26000

E. 26500

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Re: The population of city X increased by 10% in year 2013 and 15% in year  [#permalink]

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04 Jun 2020, 06:45
IMO E

Population = 21000 * (1.1)*(1.15)
= 21 * 11 * 115
= 26565
~ 26500
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Re: The population of city X increased by 10% in year 2013 and 15% in year  [#permalink]

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04 Jun 2020, 06:48
Successive percentage rate = a+b+ab/100
A = 10% (in 2013) & B = 15% (in 2014)
=> 10+15+10*15/100
=> 25+1.5 => 26.5%
The successive percentage change in 21,000 over two years
=> 21,000*126.5/100
=> 26565
Which is nearest value to 26500.
Answer should be E

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Re: The population of city X increased by 10% in year 2013 and 15% in year  [#permalink]

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04 Jun 2020, 07:44
Population in 2013 =21000
Now 10% increased in 2013 and 15% in 2014.
So population at end of 2014
21000*1.1*1.5
~26500

Hence E

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Re: The population of city X increased by 10% in year 2013 and 15% in year  [#permalink]

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04 Jun 2020, 08:02
Bunuel wrote:
The population of city X increased by 10% in year 2013 and 15% in year 2014. What is the approximate population of the city at the end of year 2014, if population of the city at the starting of year 2013 was 21,000?

A. 23000

B. 25000

C. 25500

D. 26000

E. 26500

Effective % change in population is $$10 + 15 + \frac{10*15}{100} = 25 + 1.5 = 26.50$$

Hence, Population at the end of year 2014 is $$\frac{126.50}{100}*21000$$ ~ $$26500$$, Answer must be (E)
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Re: The population of city X increased by 10% in year 2013 and 15% in year  [#permalink]

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04 Jun 2020, 10:06
Answer should be option E!

21000*1.1*1.15 = 26560

Which is Approx 26500.
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Re: The population of city X increased by 10% in year 2013 and 15% in year   [#permalink] 04 Jun 2020, 10:06

# The population of city X increased by 10% in year 2013 and 15% in year

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