If a certain sum of money invested for a certain time  amounts to Rs.350 at 5% per annum and it amounts to Rs.250 at 3% per annum. Find the time.

50 years

Amount @ 5% in t years = ₨. 350

⇒ 350 = P + \(\frac{P\;×\;5\;×\;t}{100}\)  ---(i)

Amount @ 3% in t years = ₨. 250

⇒ 250 = P + \(\frac{P\;×\;3\;×\;t}{100}\)  ---(i)

Subtracting eq.(i) from (ii)

⇒ 100 = \(\frac{P\;×\;2\;×\;t}{100}\)

⇒ \(\frac{P\;×\;t}{100}\) = 50 ---(iii)

Simple Interest @5% = \(\frac{P\;×\;5\;×\;t}{100}\)

From eq. (iii) we know,

\(\frac{P\;×\;t}{100}\) = 50

⇒ Simple Interest = 50 x 5 = ₨. 250

⇒ Principal = Amount - Simple Interest

                 = ₨.350 - ₨.250

                 = ₨.100

Again, time(T) = \(\frac{250}{100\;×\;5}\) x 100

                      = 50 years