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Question

The population of cattle in a farm increases so that the difference between the population in year n and n+2 is n+1. If the populations in year 2010, 2011 and 2013 were 39,60 and 123, respectively, then the population in 2012 was:

A
81
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B
84
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C
87
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D
90
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Solution

The correct option is C 84
Let the population in 2012 be x.

It is given that population difference between the years n and n+2 is proportional to population in the year n+1

Thus, p2013p2011p2012=p2012p2010p2011
12360x=x3960x239x=63×60

x239x3780=0
x=45,84

But, cattle population increases. Thus x=84

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