Some students (only boys and girls) from different schools appeared for an Olympiad exam. 20% of the boys and 15% of the girls failed the exam. The number of boys who passed the exam was 70 more than that of the girls who passed the exam'. A total of 90 students failed. Find the number of students that appeared for the exam.

The simple interest and the true discount on a certain sum for a given period and at a given rate are 25 and 20 respectively. The sum is 

Direction: In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x² – 2x - 8 = 0
II. y² – 7y - 60 = 0

A sum of money doubles itself in 4 years compound interest. It will amount to 8 times itself at the same rate of interest is -

If $$x=(\sqrt2+1)^{1\over3} $$, the value of $$(x^3-{1\over {x^3}}) $$ is

The ratio of milk and water in to mixtures A and B are 3:4 and 5:9 respectively. If these two mixtures are mixed in the ratio of 2:3. Then find the ratio of milk and water in the resultant mixture. 

A car can finish a certain journey in 10 hours at a speed of 42 kmph. In order to cover the same distance in 7 hours, the speed of the car (km/h) must be increased by:

If $${{k^2}\over {k^2-2k+1}}={1\over 6}$$, then what is the value of $${1\over k^3}+k3$$ ?