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6.Interest
hard
The population of a country is $10$ crore and it is the possibility that the population will become $13.31$ crore in $3$ years. What will be the annual rate per cent of this growth?
A
$8$
B
$12.7$
C
$10$
D
$15$
Solution
Given, $P=10$ crore
and population after 3 years $=13.31$ crore According to the formula,
Population after n year $=P\left(1+\frac{ R }{100}\right)^{ n }$
$\Rightarrow 13.31=10\left(1+\frac{ R }{100}\right)^{5} \Rightarrow \frac{1331}{1000}=\left(1+\frac{ R }{100}\right)^{3}$
$\Rightarrow\left(\frac{11}{10}\right)^{3}=\left(1+\frac{ R }{100}\right)^{3} \Rightarrow 1+\frac{ R }{100}=\frac{11}{10}$
$\Rightarrow \frac{ R }{100}=\frac{11}{10}-1=\frac{1}{10} \therefore R =10 \%$
Standard 13
Quantitative Aptitude
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