A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:

15%
28%
312%
415%

Answer:- 1

Explanation:-

Solution:

\begin{aligned} S . I . f o r 3 y e a r s \\ = R s . (12005 - 9800) \\ = R s . 2205. \\ S . I . f o r 5 y e a r s \\ = R s . (\frac{2205}{3} \times 5) \\ = R s . 3675 \\ ∴ Pr i n c i p a l = R s . (9800 - 3675) \\ = R s . 6125. \\ H e n c e, r a t e = (\frac{100 \times 3675}{6125 \times 5}) % \\ = 12 % \end{aligned}

$\eqalign{ & S.I.\,for\,3\,years \cr & = Rs.\,\left( {12005 - 9800} \right) \cr & = Rs.\,2205. \cr & S.I.\,for\,5\,years \cr & = Rs.\,\left( {\frac{{2205}}{3} \times 5} \right) \cr & = Rs.\,3675 \cr & \therefore \Pr incipal = Rs.\,(9800 - 3675) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,6125. \cr & Hence,\,rate = \left( {\frac{{100 \times 3675}}{{6125 \times 5}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr}$