The difference between simple interest and compound interest on a certain sum at $$ 12{1\over2}$$ % for 3 years is Rs 125. Find the sum.

A men sells his cycle at 6% profit. Had he sold it at 15% profit, he would have received 180 Rs. More. What is the cost price of the cycle?

A cask contains 24 litre mixture of wine and water in the ratio 3 : 1. How much mixture must be drawn off and replaced with water so that the quantity of wine and water becomes equal ? 

Three containers contain mixture of milk and water in the ratio 5 : 3,2 : 1 and 7 : 5 respectively . The measurement of containers are in the ratio 4 : 5 : 6. Mixture of all the containers are mixed to get a new mixture . Find the ratio of water and milk in the new mixture . 

Two numbers are in the ratio x : y . If 2 is added to both numerator and denominator ,  the fraction becomes $$ 1\over2$$. Find the value of x + y . 

Two pipes of length 36 metre and 40 metre are to be cut into equal pieces without leaving any extra length of pipe. Find the number of such pieces if pipes are to be cut of maximum length.

Sandeep buys an old scooter for Rs.4700 and spends Rs.800 on its repairs. If he sells to its Rajesh for Rs.5800, then his gain percent will be:

Find the value of given equations

$$\left({216\over1} \right) ^{-{2\over3}}÷\left({27\over1} \right) ^{-{4\over3}}=? $$