Writing a Quadratic Equation from the Given Data

Q.

At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age. Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

1. 27 years and 5 years

2. 51 years and 7 years

3. 38 years and 6 years

4. 30 years and 5 years

Q.

If $\alpha \ne \beta$and $a^2=5\alpha -3$, ${\beta }^2=5\beta -3$, then the equation having $\frac{\alpha }{\beta }$ and $\frac{\beta }{\alpha }$ as its roots is

1. $3x^2+19x+3=0$

2. $3x^2-19x+3=0$

3. $3x^2-19x-3=0$

4. $3x^2+19x+1=0$

Q.

By increasing the speed of a car by $10km/hr$, the time of journey for a distance of $72km$. is reduced by $36minutes$. Find the original speed of the car.

Q.

The age of the mother is twice the square of the age of her son. Eight years hence, the age of the mother will be $4$ years more than three times the age of her son. Find their present age.

Q.

For a rectangular field of area 3 sq. units, the length is one unit more than twice the breadth ‘x’. The quadratic equation representing the situation is:

1. $x^2$ – $2x+6=0$

2. $x^2$ – $2x+3=0$

3. $2x^2+x-3=0$

4. $2x^2+x-6=0$

Q.

Two people working together can finish the work in $\frac{22}{55}$ minutes. If one person takes 8 minutes more than the other person to finish it, find the second degree equation from which we can find time in which the faster person would finish the work.

1. $45x^2+396x-176=0$

2. $55x^2+386x-176=0$

3. $55x^2+396x-186=0$

4. $55x^2+396x-176=0$

Q.

A two digit number is such that the product of its digits is 28. When 112 is subtracted from the number, the digits interchange their places. Find the second degree equation in x from which we can find tens digit.

1. $7x^2-112x-252=0$

2. $9x^2-102x-252=0$

3. $9x^2-112x-242=0$

4. $9x^2-112x-252=0$

Q.

Find C.P if $S.PisRs18andLoss=40\%$

Q.

For a rectangular field of area 3 sq. units, the length is one unit more than twice the breadth that measures ‘x’ units. The quadratic equation representing the situation is:

1. x² – 2x + 6 = 0

2. x² – 2x + 3 = 0

3. 2x² + x - 3 = 0

4. 2x² + x - 6 = 0

Q. Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. The equation representing this situation is .

1. $(x+8)(x-55)=860$
2. $(x+8)(x+55)=860$
3. $(x-8)(x+55)=860$

Q. Ram has $x$ sweets. If 20 sweets are added to twice the number of sweets he has so that the total becomes 50, then the equation expressing this is .

1. $2x+20=50$
2. $x+40=50$
3. $x+20=100$

Q. Find a quadratic polynomial, if the zeroes of it are 2 and $-1$ respectively.

Q.

Find a natural number whose square when decreased by 84 is equal to 24 more than thrice the given number.

1. 11

2. 12

3. 14

4. 15

Q. A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. The mathematical representation to find out the number of toys produced on that day will be?
[2 Marks]

Q.

Solve each of the following equations by using inverse operations.

$a+3\frac{1}{2}=5$

Q. Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. Find the equation representing the situation.

Q.

For a rectangular field of area 3 sq. units, the length is one unit more than twice the breadth $‘x^{\prime }$. The quadratic equation representing the situation is:

1. –

2. –

3. 

4. 

Q. Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. The equation representing this situation is .

1. $(x+8)(x-55)=860$
2. $(x+8)(x+55)=860$
3. $(x-8)(x+55)=860$

Q.

For a rectangular field of area 3 sq. units, the length is one unit more than twice the breadth $‘x^{\prime }$. The quadratic equation representing the situation is:

1. $x^2$ – $2x+6=0$

2. $x^2$ – $2x+3=0$

3. $2x^2+x-3=0$

4. $2x^2+x-6=0$

Q.

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. The mathematical representation to find out the number of toys produced on that day is:

1. x² – 40x + 124 = 0

2. x² – 45x+ 324 = 0

3. x² – 55x+ 750 = 0

4. x² – 50x + 320 = 0

Q.

A boy bought a book for ₹x and sold it for ₹26. If his loss was x percent, find the second degree equation from which we can find cost price of the book.

1. $x^2-100x+3600=0$

2. $2x^2-100x+2600=0$

3. $x^2-100x+2600=0$

4. $x^2-200x+2600=0$

Q.

If a train travelled 5 km/hr faster, it would take one hour less to travel 210 km. The speed of the train is:

1. 30 km/hr

2. 35 km/hr

3. 70 km/hr

4. 60 km/hr

Q. Vijay inherits his father's wealth and squared it by starting a soft drinks company. He then starts a company which manufactures airplane toys and incurs losses amounting to $k(>0)$ times the wealth he inherits. If his total assets stand at the debt of 4 crores, then the equation representing the situation is ___.

1. $x^2-4x+4=0$
2. $x^2-kx+4=0$
3. $k{x}^2-kx-4=0$
4. $x^2-kx-k=0$

Q.

Divide 77 into two parts such that the sum of their reciprocals is $\frac{7}{12}$. From which of the following equations, we can get the required numbers? (Take one required number as x).

1. $\frac{1}{x}+\frac{1}{77-x}=\frac{7}{12}$

2. $\frac{1}{x}+\frac{1}{77-x}=\frac{12}{7}$

3. $\frac{-1}{x}+\frac{1}{77-x}=\frac{7}{12}$

4. $\frac{1}{x}+\frac{1}{77+x}=\frac{7}{12}$

Q.

In the Maths test two students, committed the following mistakes while solving a quadratic equation :
(i) One of them made a mistake in the constant term and got the roots as 2 and 4.
(ii) Another one committed an error in the coefficient of x and got the roots as 3 and 5.
But, they realised that they are wrong and they managed to get it right jointly. Find the correct quadratic equation.

1. $x^2-17x+6=0$

2. $x^2+6x+15=0$

3. $x^2+15x-6=0$

4. $x^2-6x+15=0$

Q. Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. The equation representing this situation is .

1. $(x-8)(x+55)=860$
2. $(x+8)(x+55)=860$
3. $(x+8)(x-55)=860$

Q. A boy bought a book for ₹x and sold it for ₹26. If his loss was x percent, find the second degree equation from which we can find cost price of the book.

(A) $x^2-100x+3600=0$
(B) $2x^2-100x+2600=0$
(C) $x^2-100x+2600=0$
(D) $x^2-200x+2600=0$
$\left[1\right]$

Q. If a train travelled 5 km/hr faster, it would take one hour less to travel 210 km. The speed of the train is _____. [ 3 marks]