Three pipes A, B and C can fill a cistern in 10 hours, 12 hours and 15 hours respectively. First A was opened. After 2 hour, B was opened and after 4 hours from the start of A, C was also opened. Find the time in which the cistern is just full.

$$ {Cos^4θ +Sin^4θ}={2 \over3} $$ then the value of $$ {Cos^2θ -Sin^2θ+1}$$?

If cos²α + cos²β = 2, then the value of tan³ α + sin⁵ β is :

Two places P and Q are 92 km apart. A train leaves P for Q and at the same time another train leaves Q for P. Both the trains meet 4 hrs after they start moving. If the train travelling from P to Q travels 7 km/hr faster than the other train, find the speed of the two trains.

Two trains of equal length take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 meters, in what time (in seconds) will they cross each other traveling in opposite direction? 

The MRP of a watch is Rs.4750. The shop sells it at 12% discount. If the shopkeeper had purchased the watch for Rs. 3,850, what is his gain? 

Two people, Savita and Karan, get their sales commissions based on the number of items sold each month. Their total sales commission amounts to Rs. 56,100 in a particular month. If savita got her commission 12 % higher than Karan, how much commission did Karan earn?