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

Options

A. 81
B. 84
C. 87
D. 90

Answer

B

Explanation

Year wise distribution
`2010rArr39`
`2011rArr60`
`2012rArrx`
`2013rArr123`
Let proportionality constant is 'k'
`:. ` according ti the question
`(123-60))propxrArr123-60=kk`
`rArr63=kx" "…(1)`
`" and "(x-39)prop60rArrx-39=60k" "...(2)`
solving (1) & (2)
`x^(2)-39x=60xx63`
`rArrx=84,D=129`