Manoj has ₹1612 with him.

Let the amount given to Anand be $ x $
Then, amount given to Anil = 1612 - $ x $
Rate of interest = 8% per annum (compounded annually)
Time for Anand = 13 years
Time for Anil = 14 years
Amount after 13 years for Anand = $ x(1.08)^{13} $
Amount after 14 years for Anil = $ (1612 - x)(1.08)^{14} $
Given that both final amounts are equal
$ x(1.08)^{13} = (1612 - x)(1.08)^{14} $
Dividing both sides by $ (1.08)^{13} $
$ x = (1612 - x)(1.08) $
$ x = 1740.96 - 1.08x $
$ x + 1.08x = 1740.96 $
$ 2.08x = 1740.96 $
$ x = \frac{1740.96}{2.08} $
$ x = 837 $
Amount given to Anand = ₹837