List of top Mathematics Questions on Algebra

A sum of money was divided into 2 parts in the ratio 2:5. The first part was invested for 2 years at the annual interest rate of 20% compounded annually. At what rate of simple interest per annum the second part must be invested for 2 years so that the interest earned in both cases is the same?
If \( 8^{x-1} = \left( \frac{1}{4} \right)^x \), then the value of \[ \frac{1}{\log_{x+14} x - \log_{x+15}} \div \frac{1}{\log_{1-x} 4 - \log_{1-x} 5} \] is
If a number is increased by 30% and then decreased by 20%, what is the net change?
Ten years ago, Ram was twice as old as Shyam. Ten years from now, the ratio of their ages will be 3:2. What is Ram's present age?
Given the equations \( x + y = 1 \), \( x^2 + y^2 = 2 \), \( x^5 + y^5 = A \). Let N be the number of solution pairs \( (x, y) \) to this system of equations. Then \( N \) is equal to:
If 1 man or 2 women can finish a job in 20 days, how many days will 3 men and women take to finish the same job?
If \( \alpha \) and \( \beta \) are the two roots of the equation \( x^2 + ax + b = 0 \), \( ab \neq 0 \), then the quadratic equation with roots \( \frac{1}{\alpha^3 + \alpha} \) and \( \frac{1}{\beta^3 + \beta} \) is
Let \( x \) be a positive real number such that \[ x^{8 \log_5(x) - 24} = 5^{-4} \] Then the product of all possible values of \( x \) is:
A two-digit number is such that the product of its digits is 12. If 36 is added to the number, the digits interchange their places. What is the number?
At an IIM entrepreneurship summit, two young founders, Karan and Deepak, introduced their startup. In their quirky opening, they said "The product of our ages is 240. And just like in our startup strategy, twice Deepak's age is 4 years more than Karan's age. How old was Deepak two years ago?"
The percentage change in area of a rectangle by decreasing its length and increasing its breadth by 5% is:
A number which, when increased by 15%, becomes 161. What is the original number?
Among the following expressions, the one that is a polynomial is:
If $ x = 2 $, what is the value of $ 3x^2 - 5x + 7 $?
How many solutions are there to the equation \(x_1 + x_2 + x_3 + x_4 = 17\), where \(x_1, x_2, x_3, x_4\) are nonnegative integers?

If \( |x - 6| = |x^2 - 4x| - |x^2 - 5x + 6| \), \(\text{ where \( x \) is a real variable.}\)

If \( x_k = \cos \left( \frac{2\pi k}{n} \right) + i \sin \left( \frac{2\pi k}{n} \right) \), then \[ \sum_{k=1}^{n} x_k = ? \]

If the equation \[ |x^2 - 6x + 8| = a \] \(\text{has four real solutions, then find the value of \( a \):}\)
 

If 1 is subtracted from the numerator of a fraction, then it becomes \( \frac{1}{3} \), and if 8 is added to its denominator, then it becomes \( \frac{1}{4} \). Find that fraction.
Find the values of \( x \) and \( y \) from the following equations: \[ \frac{30}{x - y} + \frac{44}{x + y} = 10 \quad \text{and} \quad \frac{40}{x - y} + \frac{55}{x + y} = 13 \]
The ratio of income of two persons is 9 : 7 and the ratio of their expenditure is 4 : 3. If each of them saves ₹ 2,000 per month, then find their monthly income.
The solution of the equation \( \frac{3}{x} - 2x = \frac{2}{x} \) will be:
Sum of areas of two squares is 117 m\(^2\). If the difference between their perimeters is 12 m, then find the sides of both the squares.
Solution of equations \( 3x + 2y = 6 \) and \( y = 0 \) will be:
Solve the following pair of equations by converting these into linear pair of equations: \[ \frac{1}{2x} - \frac{1}{3y} = 2, \quad \frac{1}{3x} + \frac{1}{2y} = \frac{13}{16}. \]