Question

Mark (✓) against the correct answer
A borrows Rs 8000 at 12% per annum simple interest and B borrows Rs 9100 at 10% per annum simple interest. In how many years will their amounts be equal?

(a) 18 years
(b) 20 years
(c) 22 years
(d) 24 years

Answer 1

(c) 22 years

$$\begin{gathered} R1=12\% \\ {R}_2=10\% \\ {P}_1=Rs.8000 \\ {P}_2=Rs.9100 \\ \mathrm{Let}\mathrm{their}\mathrm{amount}s\mathrm{be}\mathrm{equal}\mathrm{in}T\mathrm{years}. \\ {\mathrm{Amount}}_1=S.I{.}_1+P_1 \\ =\frac{P_1\times R_1\times T}{100}+P_1 \\ =\frac{8000\times 12\times T}{100}+8000 \\ =960T+8000 \\ {\mathrm{Amount}}_2=S.I{.}_2+P_2 \\ =\frac{P_2\times R_2\times T}{100}+P_2 \\ =\frac{9100\times 10\times T}{100}+9100 \\ =910T+9100 \\ {\mathrm{Amount}}_1={\mathrm{Amount}}_2 \\ \Rightarrow 960T+8000=910T+9100 \\ \Rightarrow 960T-910T=9100-8000 \\ \Rightarrow 50T=1100 \\ \Rightarrow T=22 \\ \mathrm{Hence},a\mathrm{fter}22\mathrm{years}\mathrm{their}\mathrm{amounts}\mathrm{will}\mathrm{be}\mathrm{equal}. \end{gathered}$$