Let the present ages of Ajay and Vijay be 'A' and 'V' years respectively.
A - 8 = 4/3 (V - 8) and A + 8 = 6/5 (V + 8)
3/4(A - 8) = V - 8 and 5/6(A + 8) = V + 8
V = 3/4 (A - 8) + 8 = 5/6 (A + 8) - 8
=> 3/4 A - 6 + 8 = 5/6 A + 20/3 - 8
=> 10 - 20/3 = 10/12 A - 9/12 A
=> 10/3 = A/12 => A = 40.

Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1)
Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2)
Multiplying equation (1) by 2 and subtracting it from equation (2), we get
=> 2r = 72 => r = 36.

Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.
x + 4 + x + 2 = x + 13 => x = 7
Hence three consecutive odd integers are 7, 9 and 11.

Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 360) = 2 + 2(extra)
=> 2x - 720 = x => x = 720.

Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 961
96 + 225 + 490 + 6x = 961
6x = 150 => x = 25.

Cost of each eraser = (36 + 8 -40) = Rs.4
Required amount = 15 * 36 + 12 * 45 + 10 * 8 + 5 * 4
540 + 540 + 80 + 20 = Rs.1180

If Vijay gives 'x' marbles to Ajay then Vijay and Ajay would have V - x and A + x marbles.
V - x = A + x --- (1)
If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A - 2x and V + 2x marbles.
V + 2x - (A - 2x) = 30 => V - A + 4x = 30 --- (2)
From (1) we have V - A = 2x
Substituting V - A = 2x in (2)
6x = 30 => x = 5.

Let the train fare between the two places for one person be Rs.t
Bus fare between the two places for two persons Rs.4/3 t
=> 6/2 (4/3 t) + 8(t) = 1512
=> 12t = 1512 => t = 126.

Let the number of coins of each kind be x.
=> 5x + 2x + 1x = 1152
=> 8x = 1152 => x = 144

Total distance traveled = 1800 km.
Distance traveled by plane = 600 km.
Distance traveled by bus = x
Distance traveled by train = 3x/5
=> x + 3x/5 + 600 = 1800
=> 8x/5 = 1200 => x = 750 km.