Divide ₹ 10000 in two parts so that the simple interest on the first part for 4 years at 12% per annum equals the simple interest on the second part for 4.5 years at 16% per annum.
The two parts are ₹ 6000 and ₹ 4000
Let parts be x and (10000 − x).
SI on x = (x × 12 × 4)/100 = 0.48x.
SI on (10000 − x) = ((10000 − x) × 16 × 4.5)/100 = 0.72(10000 − x).
Equating: 0.48x = 0.72(10000 − x).
0.48x = 7200 − 0.72x ⇒ 1.2x = 7200 ⇒ x = 6000.
Other part = 4000.