A sum of money doubles itself in 8 years at a certain rate of simple interest. In how many years will it become five times itself at the same rate? A16 years B24 years C32 years D40 years Show answer & explanationCorrect answer: CExplanationAmount after 8 years = 2P SI=P×R×T100A=P+SI2P=P+SISI=PP×R×8100=PR×8=100R=1008=12.5%SI = \frac{P \times R \times T}{100} \\ A = P + SI \\ 2P= P + SI \\ SI = P \\ \frac{P \times R \times 8}{100} = P \\ R \times 8 = 100 \\ R = \frac{100}{8} = 12.5\%SI=100P×R×TA=P+SI2P=P+SISI=P100P×R×8=PR×8=100R=8100=12.5% Now, when the amount becomes 5P: SI=5P−P=4PP×12.5×T100=4P12.5T100=412.5T=400T=40012.5=32SI = 5P - P = 4P \\ \frac{P \times 12.5 \times T}{100} = 4P \\ \frac{12.5T}{100} = 4 \\ 12.5T = 400 \\ T = \frac{400}{12.5} = 32 SI=5P−P=4P100P×12.5×T=4P10012.5T=412.5T=400T=12.5400=32 T = 32 years