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 the largest and smallest possible value of the number is

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

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 v…

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

Teams A, B, and C consist of five, eight, and ten members, respectively, such that every member within a team is equally productive. Working separately, teams A, B, and C can complete a certain job in 40 hours, 50 hours, and 4 hours, respectively. Two members from team A, three m…

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…

The sum of all possible real values of x for which log_(x−3)(x² − 9) = log_(x−3)(x + 1) + 2, is