At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether?

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.

Clearly, number of ways of arranging 5 books = 5 ! = 5 x 4 x 3 x 2 x 1 = 120.

So, total time taken = 120 minutes = 2 hours.

Let the total number of sweets be (25x + 8).

Then, (25x + 8) - 22 is divisible by 28

⟺ (25x - 14) is divisible by 28 ⟺ 28x - (3x + 14) is divisible by 28

⟺ (3x + 14) is divisible by 28 ⟺ x = 14.

Therefore Total number of sweets = (25 x 14 + 8) = 358.

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, out of every 16 persons, there is one captain. So, number of captains (1200/16) = 75.

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.