correct answer is: c) ₹ 12958

Explanation

Here,
Amounts = ₹ 12122
Rate = 8 % p.a.
Time = 2 years
We know, SI =\frac{P\times R\times T}{100}
And,
Amount =\ (principal\ +\ S.I)
\rightarrow Amount =\left(principle+\frac{P\times R\times T}{100}\right) _{[put S.I. value]}
\rightarrow\;₹12122=\left(p+\frac{p\;\times\;8\;\times\;2}{100}\right)
\rightarrow\;₹12122=\left(p+\frac{16p}{100}\right)
\rightarrow\;₹12122=\left(\frac{100p+16p}{100}\right)
\rightarrow\;₹12122=\frac{116p}{100}
\rightarrow\;116p=₹12122\times100 _{[cross multiply]}
\rightarrow\;116p=₹\left(\frac{12122\times100}{116}\right)
\rightarrow p = ₹ 10450
\therefore Principal = ₹ 10450
According to the question,
New time =2 years 8 months or \left(2+\frac{8}{12}\right) or \frac{8}{3} years
New rate =\ 9 % p.a.
So that
New S.I. to in 2 years 8 months at 9 % per annum will =\left(\frac{p\times t\times r}{100}\right)
\rightarrow\ \left(\frac{10450\times8\times9}{3\times100}\right)
\rightarrow\ ₹ 2508
So, New amount will be =₹\left(principal\;+\;S.I\right)
\rightarrow\ =₹\left(10450\;+\;2508\right)
\rightarrow\ ₹ 12958
Ans: In 2 years 8 months at 9 % per annum the amount will be ₹ 12958.