KVPY SA Exam 2014 Question Paper

Question : 12 of 80

Marks: +1, -0

The population of cattle in a farm increases so that the difference between the population in 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

Validate

Solution:

Year wise distribution
2010 ⇒ 39
2011 ⇒ 60
2012 ⇒ x
2013 ⇒ 123
Let proportionality constant is 'k'
∴ according to the question
(123 – 60) ∝ x ⇒ 123 – 60 = kx
⇒ 63 = kx …(1)
and (x – 39) ∝ 60 ⇒ x – 39 = 60k …(2)
solving (1) & (2)

x^2 - 39x = 60 × 63

⇒ x = 84; D = 129

Go to Question:

Prev Question

Next Question