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KVPY SA Exam 2014 Question Paper
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© examsnet.com
Question : 12
Total: 80
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
81
84
87
90
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
−
39
x
=
60
×
63
⇒ x = 84; D = 129
© examsnet.com
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