The value of $$ cot\ {π\over 20}\ cot{3π\over 20} \cot{5π\over20}\ cot{7π\over 20}\ cot {9π\over20}$$ is:

The average of eleven numbers is 68. The average of the first numbers is 78 and that of the next four number is 63. The 9^th number is two time the 11^th number and the 10^th number is 4 less than the 11^th number. What is the average of the 9^th and 11^th numbers?

An alloy contains copper and tin in the ratio 3: 2. If 250 gm of copper is added to this alloy then copper in it becomes double the quantity of tin in it. What is the amount (in gm) of tin in the alloy? 

When a number is increased by 24, it becomes 115% of itself. What is the number?

If the selling price of a product is multiplied by 2, the resulting profit is 6 times the original profit. What is the original profit percentage?

Nathu and Buchku each have certain number of oranges. Nathu says to Buckhu, " If you give me 10 of your oranges, I will have twice the number of oranges left with you “. Buckhu replies, " If you give me 10 of your oranges, I will have the same number of oranges as left with you." What is the number of oranges with Nathu and Buckhu , respectively ?