(b) \(6\frac23\) years.
S.I. for 10 years = Rs \(\bigg(1000\times\frac{5}{100}\times10\bigg)\)
= Rs 500
Principal after 10 years becomes
= Rs (1000 + 500)
= Rs 1500
Amount on that principal after t years = Rs 2000
∴ S.I. on it = Rs (2000 – 1500) = Rs 500
∴ t = \(\bigg(\frac{500\times100}{1500\times5}\bigg)\) years = \(6\frac23\) years
∴ Total time = \(\bigg(10+6\frac{2}3{}\bigg)\)years = \(6\frac23\) years.