Algebra · Textbook solutions

Quadratic Equations

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 135 questions

Standard form of quadratic equation

4 q

Solved Examples

Worked · 4
  1. Decide which of the following are quadratic equations ?
    Standard form of quadratic equation SolvedEx.1 (1)
    3x2−5x+3=03x^2 - 5x + 3 = 0
  2. Standard form of quadratic equation SolvedEx.1 (2)
    9y2+5=09y^2 + 5 = 0
  3. Standard form of quadratic equation SolvedEx.1 (3)
    m3−5m2+4=0m^3 - 5m^2 + 4 = 0
  4. Standard form of quadratic equation SolvedEx.1 (4)
    (l+2)(l−5)=0(l + 2)(l - 5) = 0

Roots of a quadratic equation

1 q

Solved Example

Worked · 1
  1. Roots of a quadratic equation SolvedEx.1
    2x2−7x+6=02x^2 - 7x + 6 = 0 check whether (i) x=32x = \dfrac{3}{2}, (ii) x=−2x = -2 are solutions of the equations.

Practice Set 2.1

17 q
  1. Ex 2.1 Q.1
    Write any two quadratic equations.
  2. Decide which of the following are quadratic equations.
    Ex 2.1 Q.2 (1)
    x2+5x−2=0x^2 + 5x - 2 = 0
  3. Ex 2.1 Q.2 (2)
    y2=5y−10y^2 = 5y - 10
  4. Ex 2.1 Q.2 (3)
    y2+1y=2y^2 + \dfrac{1}{y} = 2
  5. Ex 2.1 Q.2 (4)
    x+1x=−2x + \dfrac{1}{x} = -2
  6. Ex 2.1 Q.2 (5)
    (m+2)(m−5)=0(m + 2)(m - 5) = 0
  7. Ex 2.1 Q.2 (6)
    m3+3m2−2=3m3m^3 + 3m^2 - 2 = 3m^3
  8. Write the following equations in the form ax2+bx+c=0ax^2 + bx + c = 0, then write the values of a,b,ca, b, c for each equation.
    Ex 2.1 Q.3 (1)
    2y=10−y22y = 10 - y^2
  9. Ex 2.1 Q.3 (2)
    (x−1)2=2x+3(x - 1)^2 = 2x + 3
  10. Ex 2.1 Q.3 (3)
    x2+5x=−(3−x)x^2 + 5x = -(3 - x)
  11. Ex 2.1 Q.3 (4)
    3m2=2m2−93m^2 = 2m^2 - 9
  12. Ex 2.1 Q.3 (5)
    P(3+6p)=−5P(3 + 6p) = -5
  13. Ex 2.1 Q.3 (6)
    x2−9=13x^2 - 9 = 13
  14. Determine whether the values given against each of the quadratic equation are the roots of the equation.
    Ex 2.1 Q.4 (1)
    x2+4x−5=0x^2 + 4x - 5 = 0, x=1,−1x = 1, -1
  15. Ex 2.1 Q.4 (2)
    2m2−5m=02m^2 - 5m = 0, m=2,52m = 2, \dfrac{5}{2}
  16. Ex 2.1 Q.5
    Find kk if x=3x = 3 is a root of equation kx2−10x+3=0kx^2 - 10x + 3 = 0.
  17. Ex 2.1 Q.6
    One of the roots of equation 5m2+2m+k=05m^2 + 2m + k = 0 is −75\dfrac{-7}{5}. Complete the following activity to find the value of 'kk'. Solution : □\square is a root of quadratic equation 5m2+2m+k=05m^2 + 2m + k = 0 ∴\therefore Put m=□m = \square in the equation. 5×□2+2×□+k=05 \times \square^2 + 2 \times \square + k = 0 □+□+k=0\square + \square + k = 0 □+k=0\square + k = 0 k=□k = \square

Solutions of a quadratic equation by factorisation

5 q

Solved Examples

Worked · 5
  1. Solve the following quadratic equations by factorisation.
    Solutions of a quadratic equation by factorisation SolvedEx.1 (1)
    m2−14m+13=0m^2 - 14m + 13 = 0
  2. Solutions of a quadratic equation by factorisation SolvedEx.1 (2)
    3x2−x−10=03x^2 - x - 10 = 0
  3. Solutions of a quadratic equation by factorisation SolvedEx.1 (3)
    3y2=15y3y^2 = 15y
  4. Solutions of a quadratic equation by factorisation SolvedEx.1 (4)
    x2=3x^2 = 3
  5. Solutions of a quadratic equation by factorisation SolvedEx.1 (5)
    63 x2+7x=36\sqrt{3}\,x^2 + 7x = \sqrt{3}

Practice Set 2.2

12 q
  1. Solve the following quadratic equations by factorisation.
    Ex 2.2 Q.1 (1)
    x2−15x+54=0x^2 - 15x + 54 = 0
  2. Ex 2.2 Q.1 (2)
    x2+x−20=0x^2 + x - 20 = 0
  3. Ex 2.2 Q.1 (3)
    2y2+27y+13=02y^2 + 27y + 13 = 0
  4. Ex 2.2 Q.1 (4)
    5m2=22m+155m^2 = 22m + 15
  5. Ex 2.2 Q.1 (5)
    2x2−2x+12=02x^2 - 2x + \dfrac{1}{2} = 0
  6. Ex 2.2 Q.1 (6)
    6x−2x=16x - \dfrac{2}{x} = 1
  7. Ex 2.2 Q.1 (7)
    2 x2+7x+52=0\sqrt{2}\,x^2 + 7x + 5\sqrt{2} = 0 to solve this quadratic equation by factorisation, complete the following activity. Solution : 2 x2+7x+52=0\sqrt{2}\,x^2 + 7x + 5\sqrt{2} = 0 2 x2+□+□+52=0\sqrt{2}\,x^2 + \square + \square + 5\sqrt{2} = 0 x(……)+2(……)=0x(\ldots\ldots) + \sqrt{2}(\ldots\ldots) = 0 (……)(x+2)=0(\ldots\ldots)(x + \sqrt{2}) = 0 (……)=0(\ldots\ldots) = 0 or (x+2)=0(x + \sqrt{2}) = 0 ∴\therefore x=□x = \square or x=−2x = -\sqrt{2} ∴\therefore □\square and −2-\sqrt{2} are roots of the equation.
  8. Ex 2.2 Q.1 (8)
    3x2−26 x+2=03x^2 - 2\sqrt{6}\,x + 2 = 0
  9. Ex 2.2 Q.1 (9)
    2m(m−24)=502m(m - 24) = 50
  10. Ex 2.2 Q.1 (10)
    25m2=925m^2 = 9
  11. Ex 2.2 Q.1 (11)
    7m2=21m7m^2 = 21m
  12. Ex 2.2 Q.1 (12)
    m2−11=0m^2 - 11 = 0

Solution of a quadratic equation by completing the square

2 q

Solved Examples

Worked · 2
  1. Solution of a quadratic equation by completing the square SolvedEx.1
    Solve : 5x2−4x−3=05x^2 - 4x - 3 = 0
  2. Solution of a quadratic equation by completing the square SolvedEx.2
    Solve : x2+8x−48=0x^2 + 8x - 48 = 0

Practice Set 2.3

6 q
  1. Solve the following quadratic equations by completing the square method.
    Ex 2.3 (1)
    x2+x−20=0x^2 + x - 20 = 0
  2. Ex 2.3 (2)
    x2+2x−5=0x^2 + 2x - 5 = 0
  3. Ex 2.3 (3)
    m2−5m=−3m^2 - 5m = -3
  4. Ex 2.3 (4)
    9y2−12y+2=09y^2 - 12y + 2 = 0
  5. Ex 2.3 (5)
    2y2+9y+10=02y^2 + 9y + 10 = 0
  6. Ex 2.3 (6)
    5x2=4x+75x^2 = 4x + 7

Formula for solving a quadratic equation

5 q

Solved Examples

Worked · 5
  1. Solve quadratic equations using formula.
    Formula for solving a quadratic equation SolvedEx.1
    m2−14m+13=0m^2 - 14m + 13 = 0
  2. Formula for solving a quadratic equation SolvedEx.2
    x2+10x+2=0x^2 + 10x + 2 = 0
  3. Formula for solving a quadratic equation SolvedEx.3
    x2−2x−3=0x^2 - 2x - 3 = 0
  4. Formula for solving a quadratic equation SolvedEx.4
    25x2+30x+9=025x^2 + 30x + 9 = 0
  5. Formula for solving a quadratic equation SolvedEx.5
    x2+x+5=0x^2 + x + 5 = 0

Practice Set 2.4

10 q
  1. Compare the given quadratic equations to the general form and write values of a,b,ca, b, c.
    Ex 2.4 Q.1 (1)
    x2−7x+5=0x^2 - 7x + 5 = 0
  2. Ex 2.4 Q.1 (2)
    2m2=5m−52m^2 = 5m - 5
  3. Ex 2.4 Q.1 (3)
    y2=7yy^2 = 7y
  4. Solve using formula.
    Ex 2.4 Q.2 (1)
    x2+6x+5=0x^2 + 6x + 5 = 0
  5. Ex 2.4 Q.2 (2)
    x2−3x−2=0x^2 - 3x - 2 = 0
  6. Ex 2.4 Q.2 (3)
    3m2+2m−7=03m^2 + 2m - 7 = 0
  7. Ex 2.4 Q.2 (4)
    5m2−4m−2=05m^2 - 4m - 2 = 0
  8. Ex 2.4 Q.2 (5)
    y2+13y=2y^2 + \dfrac{1}{3}y = 2
  9. Ex 2.4 Q.2 (6)
    5x2+13x+8=05x^2 + 13x + 8 = 0
  10. Ex 2.4 Q.3
    With the help of the flow chart given below solve the equation x2+23 x+3=0x^2 + 2\sqrt{3}\,x + 3 = 0 using the formula. Flow chart : compare equations x2+23 x+3=0x^2 + 2\sqrt{3}\,x + 3 = 0 and ax2+bx+c=0ax^2 + bx + c = 0 find the values of a,b,ca, b, c →\rightarrow Find value of b2−4acb^2 - 4ac →\rightarrow Write formula to solve quadratic equation →\rightarrow Substitute values of a,b,ca, b, c and find roots.

Nature of roots of a quadratic equation

4 q

Solved examples

Worked · 4
  1. Nature of roots of a quadratic equation SolvedEx.1
    Find the value of the discriminant of the equation x2+10x−7=0x^2 + 10x - 7 = 0
  2. Determine nature of roots of the quadratic equations.
    Nature of roots of a quadratic equation SolvedEx.2 (i)
    2x2−5x+7=02x^2 - 5x + 7 = 0
  3. Nature of roots of a quadratic equation SolvedEx.2 (ii)
    x2+2x−9=0x^2 + 2x - 9 = 0
  4. Nature of roots of a quadratic equation SolvedEx.3
    3 x2+23 x+3=0\sqrt{3}\,x^2 + 2\sqrt{3}\,x + \sqrt{3} = 0

The relation between roots of the quadratic equation and coefficients

3 q

Solved examples

Worked · 3
  1. The relation between roots of the quadratic equation and coefficients SolvedEx.1
    If α\alpha and β\beta are the roots of the quadratic equation 2x2+6x−5=02x^2 + 6x - 5 = 0, then find (α+β)(\alpha + \beta) and α×β\alpha \times \beta.
  2. The relation between roots of the quadratic equation and coefficients SolvedEx.2
    The difference between the roots of the equation x2−13x+k=0x^2 - 13x + k = 0 is 7 find kk.
  3. The relation between roots of the quadratic equation and coefficients SolvedEx.3
    If α\alpha and β\beta are the roots of x2+5x−1=0x^2 + 5x - 1 = 0 then find - (i) α3+β3\alpha^3 + \beta^3 (ii) α2+β2\alpha^2 + \beta^2.

To obtain a quadratic equation having given roots

1 q

Solved examples

Worked · 1
  1. To obtain a quadratic equation having given roots SolvedEx.1
    Obtain the quadratic equation if roots are −3,−7-3, -7.

Practice Set 2.5

18 q
  1. Activity : Fill in the gaps and complete.
    Ex 2.5 Q.1 (1)
    A flow chart runs from the box "Quadratic equation ax2+bx+c=0ax^2 + bx + c = 0" to two boxes, "b2−4ac=5b^2 - 4ac = 5" and "b2−4ac=−5b^2 - 4ac = -5", and from each of those an arrow points to an empty box under the heading "Nature of roots". Fill in the two empty boxes.
  2. Ex 2.5 Q.1 (2)
    A flow chart has the box "Sum of roots =−7= -7" on the left and "Product of roots =5= 5" on the right, both pointing to a central box "Quadratic equation . . . . . . . .". Fill in the central box.
  3. Ex 2.5 Q.1 (3)
    If α\alpha, β\beta are roots of quadratic equation, a flow chart runs from the box "2x2−4x−3=02x^2 - 4x - 3 = 0" to two boxes, "α+β=……\alpha + \beta = \ldots\ldots" and "α×β=……\alpha \times \beta = \ldots\ldots". Fill in the two boxes.
  4. Find the value of discriminant.
    Ex 2.5 Q.2 (1)
    x2+7x−1=0x^2 + 7x - 1 = 0
  5. Ex 2.5 Q.2 (2)
    2y2−5y+10=02y^2 - 5y + 10 = 0
  6. Ex 2.5 Q.2 (3)
    2 x2+4x+22=0\sqrt{2}\,x^2 + 4x + 2\sqrt{2} = 0
  7. Determine the nature of roots of the following quadratic equations.
    Ex 2.5 Q.3 (1)
    x2−4x+4=0x^2 - 4x + 4 = 0
  8. Ex 2.5 Q.3 (2)
    2y2−7y+2=02y^2 - 7y + 2 = 0
  9. Ex 2.5 Q.3 (3)
    m2+2m+9=0m^2 + 2m + 9 = 0
  10. Form the quadratic equation from the roots given below.
    Ex 2.5 Q.4 (1)
    0 and 4
  11. Ex 2.5 Q.4 (2)
    3 and −10-10
  12. Ex 2.5 Q.4 (3)
    12,−12\dfrac{1}{2}, -\dfrac{1}{2}
  13. Ex 2.5 Q.4 (4)
    2−5, 2+52 - \sqrt{5}, \ 2 + \sqrt{5}
  14. Ex 2.5 Q.5
    Sum of the roots of a quadratic equation is double their product. Find kk if equation is x2−4kx+k+3=0x^2 - 4kx + k + 3 = 0
  15. α\alpha, β\beta are roots of y2−2y−7=0y^2 - 2y - 7 = 0 find,
    Ex 2.5 Q.6 (1)
    α2+β2\alpha^2 + \beta^2
  16. Ex 2.5 Q.6 (2)
    α3+β3\alpha^3 + \beta^3
  17. The roots of each of the following quadratic equations are real and equal, find kk.
    Ex 2.5 Q.7 (1)
    3y2+ky+12=03y^2 + ky + 12 = 0
  18. Ex 2.5 Q.7 (2)
    kx(x−2)+6=0kx(x - 2) + 6 = 0

Application of quadratic equation

2 q

Solved examples

Worked · 2
  1. Application of quadratic equation SolvedEx.1
    There is a rectangular onion storehouse in the farm of Mr. Ratnakarrao at Tivasa. The length of rectangular base is more than its breadth by 7 m and diagonal is more than length by 1 m. Find length and breadth of the storehouse.
  2. Application of quadratic equation SolvedEx.2
    A train travels 360 km with uniform speed. The speed of the train is increased by 5 km/hr, it takes 48 minutes less to cover the same distance. Find the initial speed of the train.

Practice Set 2.6

10 q
  1. Ex 2.6 Q.1
    Product of Pragati's age 2 years ago and 3 years hence is 84. Find her present age.
  2. Ex 2.6 Q.2
    Sum of squares of 2 consecutive natural even numbers is 244; find the numbers.
  3. Ex 2.6 Q.3
    In the orange garden of Mr. Madhusudan there are 150 orange trees. The number of trees in each row is 5 more than that in each column. Find the number of trees in each row and each column with the help of following flow chart. Flow chart : No. of trees in a column is xx →\rightarrow No. of trees in row =…= \ldots →\rightarrow Total no. of trees =……= \ldots\ldots →\rightarrow Frame quadratic equation →\rightarrow Find xx →\rightarrow No. of trees in column →\rightarrow no. of trees in a row.
  4. Ex 2.6 Q.4
    Vivek is older than Kishor by 5 years. The sum of the reciprocals of their ages is 16\dfrac{1}{6}. Find their present ages.
  5. Ex 2.6 Q.5
    Suyash scored 10 marks more in second test than that in the first. 5 times the score of the second test is the same as square of the score in the first test. Find his score in the first test.
  6. Ex 2.6 Q.6
    Mr. Kasam runs a small business of making earthen pots. He makes certain number of pots on daily basis. Production cost of each pot is ₹ 40 more than 10 times total number of pots, he makes in one day. If production cost of all pots per day is ₹ 600, find production cost of one pot and number of pots he makes per day.
  7. Ex 2.6 Q.7
    Pratik takes 8 hours to travel 36 km downstream and return to the same spot. The speed of boat in still water is 12 km. per hour. Find the speed of water current.
  8. Ex 2.6 Q.8
    Pintu takes 6 days more than those of Nishu to complete certain work. If they work together they finish it in 4 days. How many days would it take to complete the work if they work alone.
  9. Ex 2.6 Q.9
    If 460 is divided by a natural number, quotient is 6 more than five times the divisor and remainder is 1. Find quotient and diviser.
  10. Ex 2.6 Q.10
    In the adjoining fig. □ABCD\square ABCD is a trapezium AB ∥\parallel CD and its area is 33 cm2^2. From the information given in the figure find the lengths of all sides of the □ABCD\square ABCD. Fill in the empty boxes to get the solution. Figure : □ABCD\square ABCD is drawn with AB the shorter parallel side on top and DC the longer parallel side at the bottom. M is the foot of the perpendicular from A to DC, so ∠AMD=90∘\angle AMD = 90^\circ. The printed labels are AB =x= x, AM =(x−4)= (x - 4), BC =(x−2)= (x - 2), DC =(2x+1)= (2x + 1); AD and BC carry matching double tick marks, so AD == BC. Solution : □ABCD\square ABCD is a trapezium. AB ∥\parallel CD A(□ABCD)=12(AB+CD)×□A(\square ABCD) = \dfrac{1}{2}(AB + CD) \times \square 33=12(x+2x+1)×□33 = \dfrac{1}{2}(x + 2x + 1) \times \square ∴\therefore □=(3x+1)×□\square = (3x + 1) \times \square ∴\therefore 3x2+□−□=03x^2 + \square - \square = 0 ∴\therefore 3x(……)+10(……)=03x(\ldots\ldots) + 10(\ldots\ldots) = 0 ∴\therefore (3x+10)(−−−−)=0(3x + 10)(----) = 0 ∴\therefore (3x+10)=0(3x + 10) = 0 or □=0\square = 0 ∴\therefore x=−103x = -\dfrac{10}{3} or x=□x = \square But length is never negative. ∴\therefore x≠−103x \neq -\dfrac{10}{3} ∴\therefore x=□x = \square AB =−−−= ---, CD =−−−= ---, AD == BC =−−−= ---

Problem Set 2

35 q
  1. Choose the correct answers for the following questions.
    PS2 Q.1 (1)
    Which one is the quadratic equation ?
    1. A.
      5x−3=x2\dfrac{5}{x} - 3 = x^2
    2. B.
      x(x+5)=2x(x + 5) = 2
    3. C.
      n−1=2nn - 1 = 2n
    4. D.
      1x2(x+2)=x\dfrac{1}{x^2}(x + 2) = x
  2. PS2 Q.1 (2)
    Out of the following equations which one is not a quadratic equation ?
    1. A.
      x2+4x=11+x2x^2 + 4x = 11 + x^2
    2. B.
      x2=4xx^2 = 4x
    3. C.
      5x2=905x^2 = 90
    4. D.
      2x−x2=x2+52x - x^2 = x^2 + 5
  3. PS2 Q.1 (3)
    The roots of x2+kx+k=0x^2 + kx + k = 0 are real and equal, find kk.
    1. A.
      0
    2. B.
      4
    3. C.
      0 or 4
    4. D.
      2
  4. PS2 Q.1 (4)
    For 2 x2−5x+2=0\sqrt{2}\,x^2 - 5x + \sqrt{2} = 0 find the value of the discriminant.
    1. A.
      −5-5
    2. B.
      17
    3. C.
      2\sqrt{2}
    4. D.
      22−52\sqrt{2} - 5
  5. PS2 Q.1 (5)
    Which of the following quadratic equations has roots 3, 5 ?
    1. A.
      x2−15x+8=0x^2 - 15x + 8 = 0
    2. B.
      x2−8x+15=0x^2 - 8x + 15 = 0
    3. C.
      x2+3x+5=0x^2 + 3x + 5 = 0
    4. D.
      x2+8x−15=0x^2 + 8x - 15 = 0
  6. PS2 Q.1 (6)
    Out of the following equations, find the equation having the sum of its roots −5-5.
    1. A.
      3x2−15x+3=03x^2 - 15x + 3 = 0
    2. B.
      x2−5x+3=0x^2 - 5x + 3 = 0
    3. C.
      x2+3x−5=0x^2 + 3x - 5 = 0
    4. D.
      3x2+15x+3=03x^2 + 15x + 3 = 0
  7. PS2 Q.1 (7)
    5 m2−5 m+5=0\sqrt{5}\,m^2 - \sqrt{5}\,m + \sqrt{5} = 0 which of the following statement is true for this given equation ?
    1. A.
      Real and uneual roots
    2. B.
      Real and equal roots
    3. C.
      Roots are not real
    4. D.
      Three roots.
  8. PS2 Q.1 (8)
    One of the roots of equation x2+mx−5=0x^2 + mx - 5 = 0 is 2; find mm.
    1. A.
      −2-2
    2. B.
      −12-\dfrac{1}{2}
    3. C.
      12\dfrac{1}{2}
    4. D.
      2
  9. Which of the following equations is quadratic ?
    PS2 Q.2 (1)
    x2+2x+11=0x^2 + 2x + 11 = 0
  10. PS2 Q.2 (2)
    x2−2x+5=x2x^2 - 2x + 5 = x^2
  11. PS2 Q.2 (3)
    (x+2)2=2x2(x + 2)^2 = 2x^2
  12. Find the value of discriminant for each of the following equations.
    PS2 Q.3 (1)
    2y2−y+2=02y^2 - y + 2 = 0
  13. PS2 Q.3 (2)
    5m2−m=05m^2 - m = 0
  14. PS2 Q.3 (3)
    5 x2−x−5=0\sqrt{5}\,x^2 - x - \sqrt{5} = 0
  15. PS2 Q.4
    One of the roots of quadratic equation 2x2+kx−2=02x^2 + kx - 2 = 0 is −2-2, find kk.
  16. Two roots of quadratic equations are given ; frame the equation.
    PS2 Q.5 (1)
    10 and −10-10
  17. PS2 Q.5 (2)
    1−351 - 3\sqrt{5} and 1+351 + 3\sqrt{5}
  18. PS2 Q.5 (3)
    0 and 7
  19. Determine the nature of roots for each of the quadratic equation.
    PS2 Q.6 (1)
    3x2−5x+7=03x^2 - 5x + 7 = 0
  20. PS2 Q.6 (2)
    3 x2+2 x−23=0\sqrt{3}\,x^2 + \sqrt{2}\,x - 2\sqrt{3} = 0
  21. PS2 Q.6 (3)
    m2−2m+1=0m^2 - 2m + 1 = 0
  22. Solve the following quadratic equations.
    PS2 Q.7 (1)
    1x+5=1x2\dfrac{1}{x + 5} = \dfrac{1}{x^2}
  23. PS2 Q.7 (2)
    x2−3x10−110=0x^2 - \dfrac{3x}{10} - \dfrac{1}{10} = 0
  24. PS2 Q.7 (3)
    (2x+3)2=25(2x + 3)^2 = 25
  25. PS2 Q.7 (4)
    m2+5m+5=0m^2 + 5m + 5 = 0
  26. PS2 Q.7 (5)
    5m2+2m+1=05m^2 + 2m + 1 = 0
  27. PS2 Q.7 (6)
    x2−4x−3=0x^2 - 4x - 3 = 0
  28. PS2 Q.8
    Find mm if (m−12)x2+2(m−12)x+2=0(m - 12)x^2 + 2(m - 12)x + 2 = 0 has real and equal roots.
  29. PS2 Q.9
    The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.
  30. PS2 Q.10
    Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation 2x2+2(p+q)x+p2+q2=02x^2 + 2(p + q)x + p^2 + q^2 = 0
  31. PS2 Q.11
    Mukund possesses ₹ 50 more than what Sagar possesses. The product of the amount they have is 15,000. Find the amount each one has.
  32. PS2 Q.12
    The difference between squares of two numbers is 120. The square of smaller number is twice the greater number. Find the numbers.
  33. PS2 Q.13
    Ranjana wants to distribute 540 oranges among some students. If 30 students were more each would get 3 oranges less. Find the number of students.
  34. PS2 Q.14
    Mr. Dinesh owns an agricultural farm at village Talvel. The length of the farm is 10 meter more than twice the breadth. In order to harvest rain water, he dug a square shaped pond inside the farm. The side of pond is 13\dfrac{1}{3} of the breadth of the farm. The area of the farm is 20 times the area of the pond. Find the length and breadth of the farm and of the pond
  35. PS2 Q.15
    A tank fills completely in 2 hours if both the taps are open. If only one of the taps is open at the given time, the smaller tap takes 3 hours more than the larger one to fill the tank. How much time does each tap take to fill the tank completely ?