A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is

Net ascent of the monkey in 1 hour = (30 - 20) feet = 10 feet.

So, the monkey ascends 90 feet in 9 hours i.e. till 5 p.m.

Clearly, in the next 1 hour i.e. till 6 p.m. the monkey ascends remaining 30 feet to touch the flag.

Clearly, total number of handshakes = (9+ 8 + 7 + 6 + 5 + 4 + 3 + 2+1) = 45.

Let the ten's digit be x. Then, unit's digit = (11 - x).

So, number = 10x + (11 - x) = 9x + 11.

Therefore (9x + 11) + 27 = 10 (11 - x) + x ⟺ 9x + 38 = 110 - 9x ⟺ 18x = 72 ⟺ x = 4.

Thus, ten's digit = 4 and unit's digit = 7.

Hence, required number = 47.

Let the number of cows be x and the number of hens be y.

Then, 4x + 2y = 2 (x + y) + 14 ⟺ 4x + 2y = 2x + 2y + 14 ⟺ 2x = 14 ⟺ x = 7.

The seven pieces consist of 6 smaller equal pieces and one half cake piece.

Weight of each small piece = 20 g.

So, total weight of the cake = [2 x (20 x6)]g= 240 g.

Income on the first day = Re. 1.

Income on the 2nd day = Rs. (1x2) = Rs. 2¹.

Income on the 3rd day = Rs. (2¹ x 2) = Rs. 2² and so on. Thus, Income on the rath day = Rs. 2^n-1.

Therefore Income on the 10th day = Rs. 2⁹.

Let number of keepers be x. Then,

Total number of feet = 2 x 50 + 4 x 45 + 4 x 8 + 2x = 2x + 312.

Total number of heads = 50 + 45 + 8 + x= 103 + x.

Therefore (2x + 312) = (103 + x) + 224 or x = 15.

Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5. Such a number is 25.