Data Ram lends equal sum of money at the same rate of interest to A and B. The money lends to A becomes twice of the original amount in just four years at simple interest. While Data Ram lends to B for the first two years at compound interest and for the rest two years at simple interest. If the difference between the amount of A and B after 4 years is Rs. 2750. What is the amount of money that Data Ram lends to each one?
Rs. 40,000
Rs. 6,000
Rs. 8,000
Rs. 80,000
None of these
Solution
$A:~P=\dfrac{P\times 4\times r}{100}$
$\Rightarrow r = 25\%$
$B: ~P\left(1+\dfrac{25}{100}\right)^2 =\dfrac{25P}{16}$
Again $\dfrac{25P}{16}\times \dfrac{2\times 25}{100} = \dfrac{25P}{32}$
Therefore total amount of A after 4 years = 2P
and total amount of B after 4 years $=\dfrac{25P}{16}+\dfrac{25P}{32}=\dfrac{75P}{32}$
Therefore difference in amount $=\dfrac{75P}{32}-2P = \dfrac{11P}{32} = 2750$
$\Rightarrow P = 8000$