A certain amount double in 5 years, when invested at simple interest. In how many years will it become 8 times?

Let rate of interest = $$r\%$$

Let principal sum = Rs. $$100$$

Amount is doubled in 5 years = Rs. $$200$$

=> Simple interest = $$200-100=Rs.$$ $$100$$

=> $$\frac{P\times R\times T}{100}=100$$

=> $$\frac{100\times r\times5}{100}=100$$

=> $$5r=100$$

=> $$r=\frac{100}{5}=20\%$$

Now, let time required so that amount becomes 8 times = $$t$$ years

=> New interest = $$800-100=Rs.$$ $$700$$

=> $$\frac{100\times 20\times t}{100}=700$$

=> $$20t=700$$

=> $$t=\frac{700}{20}=35$$ years

=> Ans - (A)