Some students (only boys and girls) from different schools1 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 lengths of the three sides of a right-angled triangle are (x - 1) cm, (x +1) cm and (x + 3) cm, respectively. The hypotenuse of the right-angled triangle (in cm) is:

A certain sum is deposited for 4 years at a rate of 10% per annum on compound interest compounded annually. The difference between ihe interest at the end of 2 years and that at the end of 4 years is ₹5,082. Find the sum (in ₹).

The ratio of the monthly incomes of A and B is 11 : 13 and the ratio of their expenditures is 9 : 11. If both of them manage to save ₹4,000 per month, then find the difference in their incomes (in ₹).

A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:

An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor are BC and ∠CBD=40⁰. Find the measure of ∠BCD.

LCM of two numbers is 56 times their HCF, with the sum of their HCF and LCM being 1710. If one of the two numbers is 240, then what is the other number?

Find the greatest number 23a68b, which is divisible by 3 but NOT divisible by 9.