ML Aggarwal solutions for Understanding ICSE Mathematics [English] Class 10 chapter 5 - Quadratic Equations in One Variable [Latest edition]

Check whether the following are quadratic equations: `sqrt(3)x^2 - 2x + (3)/(5) = 0`

Check whether the following are quadratic equation:

(2x + 1) (3x – 2) = 6(x + 1) (x – 2)

Check whether the following are quadratic equations: `(x - 3)^3 + 5 = x^3 + 7x^2 - 1`

Check whether the following are quadratic equations: `x - (3)/x = 2, x ≠ 0`

Check whether the following are quadratic equations: `x + (2)/x = x^2, x ≠ 0`

Check whether the following are quadratic equations: `x^2 + (1)/(x^2) = 3, x ≠ 0`

In each of the following, determine whether the given numbers are roots of the given equations or not; x² – x + 1 = 0; 1, – 1

In each of the following, determine whether the given numbers are roots of the given equations or not; x² – 5x + 6 = 0; 2, – 3

In each of the following, determine whether the given numbers are roots of the given equations or not; 3x² – 13x – 10 = 0; 5, `(-2)/(3)`

In each of the following, determine whether the given numbers are roots of the given equations or not; 6x² – x – 2 = 0; `(-1)/(2), (2)/(3)`

In each of the following, determine whether the given numbers are solutions of the given equation or not: `x^2 - 3sqrt(3)x + 6 = 0; sqrt(3), -2sqrt(3)`

In each of the following, determine whether the given numbers are solutions of the given equation or not: `x^2 - sqrt(2)x - 4 = 0, x = -sqrt(2),2sqrt(2)`

If `-(1)/(2)` is a solution of the equation 3x² + 2kx – 3 = 0, find the value of k.

If `(2)/(3)`  is a solution of the equation 7x² + kx – 3 = 0, find the value of k.

If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.

If a is a root of the equation x² – (a + b)x + k = 0, find the value of k.

If `(2)/(3)` and – 3 are the roots of the equation px²+ 7x + q = 0, find the values of p and q.

Solve the following equation by factorization

4x² = 3x

Solve the following equation by factorization

`(x^2 - 5x)/(2)` = 0

Solve the following equation by factorization

(x – 3) (2x + 5) = 0

Solve the following equation by factorization

x (2x + 1) = 6

Solve the following equation by factorization

x² – 3x – 10 = 0

Solve the following equation by factorization

x(2x + 5) = 3

Solve the following equation by factorization

3x² – 5x – 12 = 0

Solve the following equation by factorization

21x² – 8x – 4 = 0

Solve the following equation by factorization

3x²= x + 4

Solve the following equation by factorization

x(6x – 1) = 35

Solve the following equation by factorization

6p²+ 11p – 10 = 0

Solve the following equation by factorization

`(2)/(3)x^2 - (1)/(3)x` = 1

Solve the following equation by factorization

(x – 4)² + 5² = 13²   

Solve the following equation by factorization

3(x – 2)² = 147

Solve the following equation by factorization

`(1)/(7)(3x  – 5)^2`= 28

Solve the following equation by factorization

3(y² – 6) = y(y + 7) – 3

Solve the following equation by factorization

x²– 4x – 12 = 0,when x∈N

Solve the following equation by factorization

2x² – 8x – 24 = 0 when x∈I

Solve the following equation by factorization

5x² – 8x – 4 = 0 when x∈Q

Solve the following equation by factorization

2x² – 9x + 10 = 0,when x∈N

Solve the following equation by factorization

2x² – 9x + 10 = 0,when x∈Q

Solve the following equation by factorization.

a²x² + 2ax + 1 = 0, a ≠ 0

Solve the following equation by factorization 

x² – (p + q)x + pq = 0

Solve the following equation by factorization

a²x² + (a²+ b²)x + b² = 0, a ≠ 0

Solve the following equation by factorization

`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0

Solve the following equation by factorization

`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0

Solve the following equation by factorization

`x^2 - (1 + sqrt(2))x + sqrt(2)` = 0

Solve the following equation by factorization

`x + (1)/x = 2(1)/(20)`

Solve the following equation by factorization

`(2)/(x^2) - (5)/x + 2 = 0, x ≠ 0`

Solve the following equation by factorization

`x^2/(15) - x/(3) - 10` = 0

Solve the following equation by factorization

`3x - (8)/x `= 2

Solve the following equation by factorization

`(x + 2)/(x + 3) = (2x - 3)/(3x - 7)`

Solve the following equation by factorization

`(8)/(x + 3) - (3)/(2 - x)` = 2

Solve the following equation by factorization

`x/(x - 1) + (x - 1)/x = 2(1)/(2)`

Solve the following equation by factorization

`x/(x + 1) + (x + 1)/x = (34)/(15)`

Solve the following equation by factorization

`(x + 1)/(x - 1) + (x - 2)/(x + 2)` = 3

Solve the following equation by factorization

`(1)/(x - 3) - (1)/(x + 5) = (1)/(6)`

Solve the following equation by factorization

`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`

Solve the following equation by factorization

`a/(ax - 1) + b/(bx - 1) = a + b, a + b ≠ 0, ab ≠ 0`

Solve the following equation by factorization

`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`

Solve the following equation by factorization

`(1)/(x + 6) + (1)/(x - 10) = (3)/(x - 4)`

Solve the following equation by factorization

`sqrt(3x + 4) = x`

Solve the following equation by factorization

`sqrt(x(x - 7)) = 3sqrt(2)`

Use the substitution y = 3x + 1 to solve for x : 5(3x + 1 )² + 6(3x + 1) – 8 = 0

Find the values of x if p + 1 =0 and x² + px – 6 = 0

Find the values of x if p + 7 = 0, q – 12 = 0 and x² + px + q = 0,

If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.

Solve the following equation by using formula :

2x² – 7x + 6 = 0

Solve the following equation by using formula:

2x² – 6x + 3 = 0

Solve the following equation by using formula :

x² + 7x – 7 = 0

Solve the following equation by using formula :

(2x + 3)(3x – 2) + 2 = 0

Solve the following equation by using formula :

256x² – 32x + 1 = 0

Solve the following equation by using formula : 

25x² + 30x + 7 = 0

Solve the following equation by using formula :

`2x^2 + sqrt(5) - 5` = 0

Solve the following equation by using formula :

`sqrt(3)x^2 + 10x - 8sqrt(3)` = 0

Solve the following equation by using formula :

`(x - 2)/(x + 2) + (x + 2)/(x - 2)` = 4

Solve the following equation by using formula :

`(x + 1)/(x + 3) = (3x + 2)/(2x + 3)`

Solve the following equation by using formula :

a (x² + 1) = (a²+ 1) x , a ≠ 0

Solve the following equation by using formula :

4x² – 4ax + (a² – b²) = 0

Solve the following equation by using formula:

`x - (1)/x = 3, x ≠ 0`

Solve the following equation by using formula :

`(1)/x + (1)/(x - 2) = 3, x ≠ 0, 2`

Solve the following equation by using formula :

`(1)/(x - 2) + (1)/(x - 3) + (1)/(x - 4)` = 0

Solve:

`2((2x - 1)/(x + 3)) - 3((x + 3)/(2x - 1)) = 5; x ≠ -3, (1)/(2)`

Solve the following equation by using quadratic equations for x and give your x² – 5x – 10 = 0

Solve the following equation by using quadratic equations for x and give your 5x(x + 2) = 3

Solve the following equation for x and give, in the following case, your answer correct to 2 decimal places:

4x² – 5x – 3 = 0

Solve the following equation by using quadratic formula and give your answer correct to 2 decimal places : `2x - (1)/x = 1`

Solve the following equation: `x - (18)/x = 6`. Give your answer correct to two x significant figures.

Solve the equation 5x² – 3x – 4 = 0 and give your answer correct to 3 significant figures:

Find the discriminant of the following equations and hence find the nature of roots: 3x² – 5x – 2 = 0

Find the discriminant of the following equations and hence find the nature of roots: 2x²– 3x + 5 = 0

Find the discriminant of the following equations and hence find the nature of roots: 7x² + 8x + 2 = 0

Find the discriminant of the following equations and hence find the nature of roots: 3x² + 2x - 1 = 0

Find the discriminant of the following equations and hence find the nature of roots: 16x² - 40x +  25 = 0

Find the discriminant of the following equations and hence find the nature of roots: 2x² + 15x + 30 = 0

Discuss the nature of the roots of the following quadratic equations : x² – 4x – 1 = 0

Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0

Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 0

Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0

Discuss the nature of the roots of the following quadratic equations : -2x² + x + 1 = 0

Discuss the nature of the roots of the following quadratic equations : `2sqrt(3)x^2 - 5x + sqrt(3)` = 0

Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0

Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.

Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: px² – 4x + 3 = 0

Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: x² + (p – 3)x + p = 0.

Find the value (s) of k for which each of the following quadratic equation has equal roots : kx² – 4x – 5 = 0

Find the value (s) of k for which each of the following quadratic equation has equal roots : (k – 4) x² + 2(k – 4) x + 4 = 0

Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x² + 2(m + 1)x + m = 0

Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x² + 2(m – 1) x + (m + 5) = 0

Find the values of k for which each of the following quadratic equation has equal roots: 9x² + kx + 1 = 0 Also, find the roots for those values of k in each case.

Find the values of k for which each of the following quadratic equation has equal roots: x² – 2kx + 7k – 12 = 0 Also, find the roots for those values of k in each case.

Find the value(s) of p for which the quadratic equation (2p + 1)x² – (7p + 2)x + (7p – 3) = 0 has equal roots. Also find these roots.

If – 5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x) + k = 0 has equal roots, find the value of k.

Find the value(s) of p for which the equation 2x² + 3x + p = 0 has real roots.

Find the least positive value of k for which the equation x² + kx + 4 = 0 has real roots.

Find the values of p for which the equation 3x² – px + 5 = 0 has real roots.

Find two consecutive natural numbers such that the sum of their squares is 61.

Find two consecutive integers such that the sum of their squares is 61

If the product of two positive consecutive even integers is 288, find the integers.

If the product of two consecutive even integers is 224, find the integers.

Find two consecutive even natural numbers such that the sum of their squares is 340.

Find two consecutive odd integers such that the sum of their squares is 394.

The sum of two numbers is 9 and the sum of their squares is 41. Taking one number as x, form ail equation in x and solve it to find the numbers.

Five times a certain whole number is equal to three less than twice the square of the number. Find the number.

Sum of two natural numbers is 8 and the difference of their reciprocal is 2/15. Find the numbers.

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

There are three consecutive positive integers such that the sum of the square of the first and the product of other two is 154. What are the integers?

Find three successive even natural numbers, the sum of whose squares is 308.

Find three consecutive odd integers, the sum of whose squares is 83.

In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.

The sum of the numerator and denominator of a certain positive fraction is 8. If 2 is added to both the numerator and denominator, the fraction is increased by `(4)/(35)`. Find the fraction.

A two digit number contains the bigger at ten’s place. The product of the digits is 27 and the difference between two digits is 6. Find the number.

A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.

A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that the perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.

A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.

Harish made a rectangular garden, with its length 5 metres more than its width. The next year, he increased the length by 3 metres and decreased the width by 2 metres. If the area of the second garden was 119 sq m, was the second garden larger or smaller ?

The length of a rectangle exceeds its breadth by 5 m. If the breadth were doubled and the length reduced by 9 m, the area of the rectangle would have increased by 140 m². Find its dimensions.

The perimeter of a rectangular plot is 180 m and its area is 1800 m². Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.

The lengths of the parallel sides of a trapezium are (x + 9) cm and (2x – 3) cm and the distance between them is (x + 4) cm. If its area is 540 cm², find x.

If the perimeter of a rectangular plot is 68 m and the length of its diagonal is 26 m, find its area.

If the sum of two smaller sides of a right – angled triangle is 17cm and the perimeter is 30cm, then find the area of the triangle.

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

Mohini wishes to fit three rods together in the shape of a right triangle. If the hypotenuse is 2 cm longer than the base and 4 cm longer than the shortest side, find the lengths of the rods.

In a P.T. display, 480 students are arranged in rows and columns. If there are 4 more students in each row than the number of rows, find the number of students in each row.

In an auditorium, the number of rows are equal to the number of seats in each row.If the number of rows is doubled and number of seats in each row is reduced by 5, then the total number of seats is increased by 375. How many rows were there?

At an annual function of a school, each student gives the gift to every other student. If the number of gifts is 1980, find the number of students.

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be 'x' km/h, form an equation and solve it to evaluate 'x'.

The speed of an express train is x km/hr arid the speed of an ordinary train is 12 km/hr less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train.

A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/hr more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.

An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for:

1. the onward journey;
2. the return journey.

If the return journey took 30 minutes less than the onward journey, write down an equation in x and find its value.

The distance by road between two towns A and B is 216 km and by rail it is 208 km. A car travels at a speed of x km/hr and the train travels at a speed which is 16 km/hr faster than the car. Calculate:

1. the time taken by the car to reach town B from A, in terms of x;
2. the time taken by the train to reach town B from A, in terms of x.
3. If the train takes 2 hours less than the car, to reach town B, obtain an equation in x and solve it.
4. Hence, find the speed of the train.

An aeroplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km, than what it would have taken to fly against the same wind. Find the planes speed of flying in still air.

A school bus transported an excursion party to a picnic spot 150 km away. While returning, it was raining and the bus had to reduce its speed by 5 km/hr, and it took one hour longer to make the return trip. Find the time taken to return.

A boat can cover 10 km up the stream and 5 km down the stream in 6 hours. If the speed of the stream is 1.5 km/hr. find the speed of the boat in still water.

Two pipes running together can fill a tank in `11(1)/(9)` minutes. If one pipe takes 5 minutes more than the other to fill the tank, find the time in which each pipe would/fill the tank.

Rs. 480 is divided equally among ‘x’ children. If the number of children were 20 more then each would have got Rs. 12 less. Find ‘x’.

Rs. 7500 is divided equally among a certain number of children. Had there been 20 less children, each would have receive Rs 100 more. Find the original number of children. 

2x articles cost Rs. (5x + 54) and (x + 2) similar articles cost Rs. (10x – 4), find x.

A trader buys x articles for a total cost of Rs. 600.

1. Write down the cost of one article in terms of x. If the cost per article were Rs. 5 more, the number of articles that can be bought for Rs. 600 would be four less.
2. Write down the equation in x for the above situation and solve it for x.

A shopkeeper buys a certain number of books for Rs 960. If the cost per book was Rs 8 less, the number of books that could be bought for Rs 960 would be 4 more. Taking the original cost of each book to be Rs x, write an equation in x and solve it to find the original cost of each book.

A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?

The hotel bill for a number of people for an overnight stay is Rs. 4800. If there were 4 more, the bill each person had to pay would have reduced by Rs. 200. Find the number of people staying overnight. 

A person was given Rs. 3000 for a tour. If he extends his tour programme by 5 days, he must cut down his daily expenses by Rs. 20. Find the number of days of his tour programme.

Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.

The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages.

Paul is x years old and his father’s age is twice the square of Paul’s age. Ten years hence, the father’s age will be four times Paul’s age. Find their present ages.

The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find the present age.

Two years ago, a man’s age was three times the square of his daughter’s age. Three years hence, his age will be four times his daughter’s age. Find their present ages.

The length (in cm) of the hypotenuse of a right-angled triangle exceeds the length of one side by 2 cm and exceeds twice the length of another side by 1 cm. Find the length of each side. Also, find the perimeter and the area of the triangle.

If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 cm². However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm². Determine the sides of the two squares.

Choose the correct answer from the given four options :

Which of the following is not a quadratic equation?

Choose the correct answer from the given four options :

Which of the following is a quadratic equation?

Which of the following equations has 2 as a root?

If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.

Choose the correct answer from the given four options :

If `(1)/(2)` is a root of the quadratic equation 4x² – 4kx + k + 5 = 0, then the value of k is

Choose the correct answer from the given four options :

The roots of the equation x² – 3x – 10 = 0 are

Choose the correct answer from the given four options :

If one root of a quadratic equation with rational coefficients is `(3 - sqrt(5))/(2)`, then the other

Choose the correct answer from the given four options :

If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is

Choose the correct answer from the given four options :

The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)

Choose the correct answer from the given four options :

If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)

Choose the correct answer from the given four options :

If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are

Choose the correct answer from the given four options :

If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by

The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.

Choose the correct answer from the given four options :

Which of the following equations has two distinct real roots?

Which of the following equations has no real roots?

Solve the following equation by factorisation :

x2 + 6x – 16 = 0

Solve the following equation by factorisation :

3x² + 11x + 10 = 0

Solve the following equation by factorisation :

2x² + ax – a²= 0

Solve the following equation by factorisation :

`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0

Solve the following equation by factorisation :

x(x + 1) + (x + 2)(x + 3) = 42

Solve the following equation by factorisation :

`(6)/x - (2)/(x - 1) = (1)/(x - 2)`

Solve the following equation by factorisation :

`sqrt(x + 15) = x + 3`

Solve the following equation by factorisation :

`sqrt(3x^2 - 2x - 1) = 2x - 2`

Solve the following equation by using formula :

2x² – 3x – 1 = 0

Solve the following equation by using formula :

`x(3x + 1/2)` = 6

Solve the following equation by using formula :

`(2x + 5)/(3x + 4) = (x + 1)/(x + 3)`

Solve the following equation by using formula :

`(2)/(x + 2) - (1)/(x + 1) = (4)/(x + 4) - (3)/(x + 3)`

Solve the following equation by using formula :

`(3x - 4)/(7) + (7)/(3x - 4) = (5)/(2), x ≠ (4)/(3)`

Solve the following equation by using formula :

`(4)/(3) - 3 = (5)/(2x + 3), x ≠ 0, -(3)/(2)`

Solve the following equation by using formula :

x² + (4 – 3a)x – 12a = 0

Solve the following equation by using formula :

10ax² – 6x + 15ax – 9 = 0,a≠0

Solve for x using the quadratic formula. Write your answer correct to two significant figures:

(x – 1)² – 3x + 4 = 0

Discuss the nature of the roots of the following equation: 3x² – 7x + 8 = 0

Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0

Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0

Discuss the nature of the roots of the following equation: `sqrt(3)x^2 - 2x - sqrt(3)` = 0

Find the values of k so that the quadratic equation (4 – k) x² + 2 (k + 2) x + (8k + 1) = 0 has equal roots.

Find the values of m so that the quadratic equation 3x² – 5x – 2m = 0 has two distinct real roots.

Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx² = 4(kx – 1)

Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x² + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.

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

Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.

Two natural numbers are in the ratio 3 : 4. Find the numbers if the difference between their squares is 175.

Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.

The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.

A farmer wishes to grow a 100 m² rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side fence. Find the dimensions of his garden.

The hypotenuse of a right-angled triangle is 1 m less than twice the shortest side. If the third side is 1 m more than the shortest side, find the sides of the triangle.

A wire ; 112 cm long is bent to form a right angled triangle. If the hypotenuse is 50 cm long, find the area of the triangle.

Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
(i) Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
(ii) If car A uses 4 litres of petrol more than car B in covering 400 km. write down an equation, in A and solve it to determine the number of litres of petrol used by car B for the journey.

The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream

By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.

A man spent Rs. 2800 on buying a number of plants priced at Rs x each. Because of the number involved, the supplier reduced the price of each plant by Rupee 1.The man finally paid Rs. 2730 and received 10 more plants. Find x.

Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.