correct answer is: c) ₹ 1080 and ₹ 1920

Explanation

Let, 1 ^st part is ₹ x
So 2 ^nd part is ₹\left(3000\;-\;x\right)
We know, S.I. =\left(\frac{p\times r\times t}{100}\right)
In 1 ^st case,
P = ₹ x
R = 8 %
T = 4 years
\therefore S.I. =₹\left(\frac{x\times8\times4}{100}\right)
\rightarrow S.I. =₹\frac{32x}{100}
In 2 ^nd case,
P =₹\left(3000\;-\;x\right)
R = 9 %
T = 2 years
\therefore S.I. =₹\{\frac{\left(3000-x\right)\times9\times2}{100}\}
\rightarrow S.I. =₹\left(\frac{54000\ -\ 18x}{100}\right)
According to the question,
₹ \left(\frac{32x}{100}\right)\ =₹\left(\frac{54000\ -\ 18x}{100}\right) _{[same denominator]}
\rightarrow\;32x=₹\left(54000-18x\right)
\rightarrow\ 32x+18x=₹54000
\rightarrow\ 50x=₹ 54000
\rightarrow\ x=₹\frac{54000}{50}
\rightarrow\ x = ₹ 1080
\therefore 1 ^st part is ₹ x or ₹ 1080
and 2 ^nd part is ₹\left(3000\;-\;x\right) or ₹\left(3000-1080\right) or ₹ 1920
Ans: One part ₹ 1080 & Second part ₹ 1920 .