ICSE Class 10th Mathematics Chapter 6 - Solving Simple Problems based on quadratic equations Important Questions with Answers

Three positive numbers are in the ratio `1/2 : 1/3 : 1/4`. Find the numbers if the sum of their squares is 244.

Divide 20 into two parts such that three times the square of one part exceeds the other part by 10.

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Assume the middle number to be x and form a quadratic equation satisfying the above statement. Hence; find the three numbers.

Out of three consecutive positive integers, the middle number is p. If three times the square of the largest is greater than the sum of the squares of the other two numbers by 67; calculate the value of p.

A can do a piece of work in ‘x’ days and B can do the same work in (x + 16) days. If both working together can do it in 15 days. Calculate ‘x’.

One pipe can fill a cistern in 3 hours less than the other. The two pipes together can fill the cistern in 6 hours 40 minutes. Find the time that each pipe will take to fill the cistern.

A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.

The sides of a right-angled triangle containing the right angle are 4x cm and (2x – 1) cm. If the area of the triangle is 30 cm²; calculate the lengths of its sides.

The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.

The sides of a right-angled triangle are (x – 1) cm, 3x cm and (3x + 1) cm. Find:

1. the value of x,
2. the lengths of its sides,
3. its area.