The simple interest on a certain sum for 2 years at a certain rate of interest is Rs.2000 and compound interest on the same sum, same time and same rate of interest is Rs.2050. Then find the ratio between CI for 2 years and CI for 3 years?

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

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? 

A merchant marks his goods at Rs. 900 and allows a discount of 25%. If he still gain 12.5%, then the cost price of the article is

If a + b + c = 12, a² + b² + c² = 52, then what is ab + bc + ca equal to-

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.

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? 

In a test consisting of 150 questions carrying 1 mark each, Saurabh answered 80 % of the first 75 question correctly. What percent of the other 75 question does he need to answer correctly to score 60 % overall?