Frank solutions for Mathematics - Part 2 [English] Class 10 ICSE chapter 7 - Problems Based On Quadratic Equations [Latest edition]

The sum of the square of the 2 consecutive natural numbers is 481. Find the numbers.

The sum of 2 numbers is 18. If the sum of their reciprocals is `1/4` , find the numbers. 

The sum of a number and its reciprocal is `2 9/40`. Find the number. 

A two digit number is such that its product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.

A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.

The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.

The difference of the square of two natural numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.

A two digit number is four times the sum and 3 times the product of its digits, find the number.

Two natural numbers differ by 4. If the sum of their square is 656, find the numbers.

The sum of the square of 2 consecutive odd positive integers is 290.Find them.

Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.

The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.

Find two natural numbers which differ by 3 and whose squares have the sum of 117.

A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.

A two digit number is such that the product of the digit is 12. When 36 is added to the number, the digits interchange their places. Find the numbers.

A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.

Three years ago, a man was 5 times the age of his son. Four years hence, he will be thrice his son's age. Find the present ages of the man and his son.

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Determine their present ages.

The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.

The product of a girl's age five years ago and her age 3 years later is 105. Find her present age.

The hypotenuse of a right-angled triangle is 17cm. If the smaller side is multiplied by 5 and the larger side is doubled, the new hypotenuse will be 50 cm. Find the length of each side of the triangle.

The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.

The length of the sides forming a right angle in a triangle are 5x cm and (3x-1) cm. If the area of the triangle is 60cm², find the hypotenuse.

The area of right-angled triangle is 600cm². If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.

The area of the isosceles triangle is 60 cm², and the length of each one of its equal side is 13cm. Find its base. 

The perimeter of the right angled triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle. 

A farmer wishes to grow a 100m² rectangular vegetable garden. Since he was with him only 30m barbed wire, he fences 3 sides of the rectangular garden letting the compound of his house to act as the 4th side. Find the dimensions of his garden .

The perimeter of a rectangular field is 82m and its area is 400m2, find the dimension of the rectangular field. 

There is a square field whose side is 44m. A square flower bed is prepared in its centre leaving a gravel path all round the flower bed. The total cost of laying the flower bed and graving the path at Rs 2. 75 and Rs. 1.5 per square metre, respectively, is Rs 4,904. Find the width of the gravel path. 

The length of a hall is 5 m more than the breadth. If the area of the floor of the hall is 84m2, find the length and breadth of the hall. 

A takes 6 days less than the time taken by B to finish a piece of work. If both A and B work together they can finish in 4 days. Find the time taken by B to finish the work. 

A takes 10days less than B to Finish a piece of work , If both A and B work together , they can finish the work in 12 days. Find the time taken by B to finish the work.

A train travels a distance of 300kms at a constant speed. If the speed of the train is increased by 10km/ hour, the j ourney would have taken 1 hour less. Find the original speed of the train.

A fast train takes 3 hours less than a slow train for a journey of 600kms. If the speed of the slow train is 1 Okm/ hr less than the fast train, find the speed of the fast train. 

An ordinary train takes 3 hours less for a j ourney of 360kms when its speed is increased by 1 Okm/ hr.Fnd the usual speed of the train. 

The time taken by a person to cover 150kms was 2.5 hrs more than the time taken in the return j ourney. If he returned at a speed of 10km/ h more than the speed when going, find his speed per hour in each direction. 

The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.

The speed of the boat in still water is 11 km/ hr. It can go 21 km upstream and 12 km downstream in 3 hours. Find the speed of the stream. 

In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of the flight increased by 30 minutes. Find the scheduled duration of the flight.

A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600kms away in time, it had to incease its speed by 400km/ hr from its usual speed. Find the usual speed of the plane. 

An aeroplane takes 1 hour less for a journey of 1200km, if its speed is increased by 100km/ hrfrom its usual speed. Find the usual speed.

A piece of cloth cost Rs 5000. If the cost price of the cloth was Rs 5 less per meter, SOm more of the cloth would have been purchased. Find the cost price per meter of cloth and length of the cloth purchased. 

A scholarship account of Rs 75,000 was distributed equally among a certain number of students. Had there been 10 students more, each would have got Rs 250 less. Find the original number of persons. 

A shopkeeper buys a number of books for Rs 840. If he had bought 5 more books for the same amount, each book would have cost Rs 4 less. How many books did he buy? 

One fourth of herd of camel was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camel.

The angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown by Bheeshm on him and with six other arrows, he killed the chariot driver of Bheeshm. With one arrow each, he knocked down respectively the chariot, the flag and the bow of Bheeshm. Finally, with one more than 4 times the square root of arrows, he laid below Bheeshm unconscious on the arrow bed. Find the total number of arrows Arjun had.

Out of a group of Swans, 3 and half times the square root of the total number are playing on the shore of a pond. The two remaining ones are swinging in water. Find the total number of swans.