A certain sum becomes 7 times in 8 years, at simple interest, then in how many years it will become 19 times?

Let principal sum = Rs. $$P$$ and rate of interest = $$r\%$$

Amount under simple interest after 8 years = $$P+\frac{P\times R\times T}{100}$$

=> $$P+(\frac{P\times r \times8}{100})=7P$$

=> $$\frac{8r}{100}=7-1=6$$

=> $$r=\frac{600}{8}=75\%$$

Let after $$t$$ years it becomes 19 times

=> $$P+(\frac{P\times 75 \times t}{100})=19P$$

=> $$\frac{75t}{100}=19-1=18$$

=> $$t=\frac{1800}{75}=24$$

$$\therefore$$ After 24 years, the sum becomes 19 times.

=> Ans - (D)