Q. The sum of the reciprocals of Rehman’s ages (in years) 3 years ago and 5 years from now is 1/3 . Find his present age. Ans: Let’s consider Rehman’s present age be X Hence, his age 3 years ago = X – 3 and his age 5 years from now = X + 5 […]

Q. In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects. Ans: Let’s consider the marks in mathematics be X.

Q. The diagonal of rectangular field is 60 meters more than the shorter side. If the longer side is 30 m more than the shorter side, find the sides of the field. Ans: Let’s consider the shorter side of the field be X m. Hence, the longer side will be (X + 30) m (by

Q. Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Ans: (note: In this question, we justify the answer with proper reason) Let’s consider the ages of friends as X years

Q. Is it possible to design a rectangular park of perimeter 80m and the area 400 m2? If so, find the length and breadth. Ans: Let’s consider the length of rectangular as X m and width as Y m. By given 1st condition, its perimeter is 80m By given 2nd condition, its area is 400

Q. Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find the length and breadth. Ans: Let’s consider the length of rectangular as X m and width as Y m. By given 1st condition, its length is twice its breadth… …..

Q. Find the values of k for following quadratic equation, so that it has equal roots: kx (x -2) + 6 = 0 Ans: Given quadratic equation: kx (x – 2) + 6 = 0 by simplifying this we get kx2 – 2 kx + 6 = 0 Let’s compare the given equation with standard

Q. Find the values of k for following quadratic equation, so that it has equal roots: 2×2 + kx + 3 = 0 Ans: Let’s compare the given equation with standard quadratic equation: Standard quadratic equation: a x2 + bx + c = 0 Given quadratic equation: 2×2 + kx + 3 = 0 By comparing these two

Q. Sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, find the sides of the two squares. Ans: Let consider the sides of the two squares be x m and y m. We know that the area of a square is given by: Hence, area

Q. An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/h more than that of the passenger train, find the average speed of the