Mathematics Questions

Solve for x and y: ax + by = a-b and bx - ay = a+b.

A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How long would A take to do the work alone?

Find the values of x and y using the method of cross-multiplication.

The sum of digits of a two-digit number is 12. The number obtained by interchanging the digits exceeds the given number by 18. Find the number.

For what value of k does the system have a unique solution?

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. Student A takes food for 20 days and pays Rs 1000. Student B takes food for 26 days and pays Rs 1180. Find the fixed charge.

Solve for x: (x-a)/(b+c) + (x-b)/(c+a) + (x-c)/(a+b) = 3.

If 37x + 43y = 123 and 43x + 37y = 117, find x and y.

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

Solve for x and y: 2/(3x+2y) + 3/(3x-2y) = 17/5 and 5/(3x+2y) + 1/(3x-2y) = 2.

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the father's age.

Points A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If they travel in the same direction, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What is the speed of the faster car?

Solve for x: 1/(x+1) + 1/(x+2) = 2/(x+10). (Though simplified it involves x^2, certain forms at SEE level are treated via logic).

In a triangle ABC, angle C = 3 * angle B = 2 * (angle A + angle B). Find angle B.

Find the values of x and y that satisfy: 4x + 6/y = 15 and 6x - 8/y = 14.

If the length of a rectangle is reduced by 5 units and breadth is increased by 3 units, the area is reduced by 9 sq units. If we increase length by 3 and breadth by 2, area increases by 67. Find length.

Solve: 3^(x+y) = 243 and 243^(x-y) = 3. Find x.

If x + y = a + b and ax - by = a^2 - b^2, then y is:

What is the value of x in 2x/3 - (x-1)/6 = 1?

Solve for x: 1/2(x+1) + 1/3(x-1) = 5/12(x-2). (Checking SEE patterns for hard linear).