Theory of Equat...

Karan and Nikhil are basketball players. Their ratio of shooting the ball to the basket is 8 : 3, where Karan shoots 8 balls when Nikhil shoots 3. But, Karan converts one basket in four shots, while Nikhil converts one basket in two shots. If Nikhil has missed 39 shots, how many shots has Karan converted?

The taxi charges in a city comprise of a fixed charge with the charge for the distance covered. For a journey of 10 km, the charge paid is Rs. 75 and for a journey of 15 km, the charge paid is Rs. 110. What will a person have to pay for travelling a distance of 25 km?

When you reverse the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

How many pairs of positive integers (m, n) satisfy , where n is an odd integer less than 60?

In a shop, the cost of 3 burgers, 7 milkshakes and French fries is Rs. 120. In the same shop, the cost of 4 burgers, 10 milkshakes and French fries is Rs. 164.5. Find the cost of 1 burger, 1 milkshake and French fries in the shop.

A two digit number becomes five-sixth of itself if the digits are reversed. The two digits differ by one. The number is

How many positive integer pairs (a, b) satisfy the equation ab = a + b + 20?

The number of solutions of the equation 7x + 3y = 123, where x, y > 0, is

A piece of string is 40 cm long. It is cut into three pieces. The longest piece is three times as long as the middle-sized and the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece.

A businessman knows that the price of a commodity will increase by Rs. 5 per packet. He bought some packets of the commodity for Rs. 4,500. If he bought them on new price, then he got 10 packets less. Find the number of packets bought by him.

The number of ordered pairs of natural numbers (x, y) satisfying the equation 2x + 3y = 100 is

Examine the nature of roots of
(i) x² + 9x + 27 = 0
(ii) 6x² - 13x - 5 = 0

How many integral roots does the equation x – = 3 – have?

Which one of the following pairs cannot be the roots of the quadratic equation?

The square of one-eighth of a number when added to 12 results in the number itself. Find the number.

If 9^z - 10 × 3^z + 9 = 0, then z is equal to

Two farmers Ravi and Ram have 40 goats in total. They sell their goats at different prices, but each of them receives the same amount of sum. If Ravi had sold his goats at Ram's price, he would have received Rs. 5400. If Ram had sold his goats at Ravi's price, he would have received Rs. 2400. How many goats does Ravi have in total?

If the roots of the equation ax² + bx + c = 0 are in the ratio of m : n, where b = c, then the value of + + is

If α and β are the roots of the equation |x|² + |x| - 6 = 0, then

If both x and y are real, and x² + y² + 2x – 10y = –26, then find the value of x + y.