Vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. A certain volume is taken out from A and poured into B. After stirring, the same volume is taken out from B and poured into A. If the resultant ratio of alcohol and water in A is 15 : 4, then the volume, in litres, initially taken out from A is

If 12^(12x) × 4^(24x+12) × 5^(2y) = 8^(4z) × 20^(12x) × 243^(3x−6), where x, y and z are natural numbers, then x + y + z equals

In a school with 1500 students, each student chooses any one of the streams out of science, arts, and commerce, by paying a fee of Rs.1100, Rs. 1000, and Rs.800, respectively. The total fee paid by all the students is Rs.15,50,000. If the number of science students is not more th…

The average salary of 5 managers and 25 engineers in a company is 60000 rupees. If each of the managers received 20% salary increase while the salary of the engineers remained unchanged, the average salary of all 30 employees would have increased by 5%. The average salary, in rup…

For a 4-digit number (greater than 1000), sum of the digits in the thousands, hundreds, and tens places is 15. Sum of the digits in the hundreds, tens, and units places is 16. Also, the digit in the tens place is 6 more than the digit in the units place. The difference between th…

ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and AB = 3DC. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is

The sum of all the digits of the number (10⁵⁰ + 10²⁵ − 123), is

The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed marked price was used for the product in all the four months. Discounts of 20%, 10% and 5% were given on the marked…

If f(x) = (x² + 3x)(x² + 3x + 2), then the sum of all real roots of the equation √(f(x) + 1) = 9701, is