A motorboat whose speed is 20 km/h in still water takes 30 minutes more to go 24 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 2 km/h, then bow much time will it take to go 39 km downstream and 30 km upstream?

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.

A sphere of radius 5 cm is melted to form a cone with base of same radius. The height (in cm) of the cone is

If x = z = 225 and y = 226 then the value of : x³ + y³ + z³ – 3xyz is

If x² + x = 5 then the value of   $${(x+3)^3}+{1\over (x+3)^3}$$ is

In an isosceles triangle, if the unequal angle is twice the sum of the equal angles, then each equal angle is

One acute angle of a right-angled triangle is double the other. If the length of its hypotenuse is 10 cm, then its area is

If m = – 4, n = – 2, then the value of m³ – 3m² + 3m + 3n + 3n² + n³ is