Linear Equation


  1. The cost of 2 sarees and 4 shirts is ₹ 16000 while 1 saree and 6 shirts cost the same. The cost of 12 shirts is











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    Let cost of one saree and shirt be x and y, respectively.
    2x + 4y = 16000 ....(i)
    x + 6y = 16000 ....(ii)

    Solve above equations and find y
    And finally cost of 12 shirts = 12y

    Correct Option: B

    Let cost of one saree and shirt be x and y, respectively.
    2x + 4y = 16000 ....(i)
    x + 6y = 16000 ....(ii)

    On multiplying Eq. (ii) by 2 and subtracting from Eq. (i). we get
    2x + 4y = 16000
    2x + 12y = 32000
    -------------------------
    -8y = -16000
    ∴ y = 2000

    Putting the value of y in Eq. (ii), we get
    x +6 x 2000 = 16000
    ∴ x = 4000
    ∴ Cost of 12 shirts = 12y
    = 12 x 2000 = ₹ 24000


  1. The system of equations 3x + y - 4 = 0 and 6x + 2y - 8 = 0 has









  1. View Hint View Answer Discuss in Forum

    Given equations of system
    3x + y = 4 ...(i)
    x + 2y = 8 ...(ii)
    Here, a1 = 3 , b2 = 2 and c2 = B
    ∵ a1/a2 = b1/b2 = c1/c2 = 1/2
    So, the system of equations has infinite solutions, because it represents a parallel line.

    Correct Option: D

    Given equations of system
    3x + y = 4 ...(i)
    x + 2y = 8 ...(ii)
    Here, a1 = 3 , b2 = 2 and c2 = B
    ∵ a1/a2 = b1/b2 = c1/c2 = 1/2
    So, the system of equations has infinite solutions, because it represents a parallel line.



  1. If 6x - 10y = 10 and x / (x + y) = 5/7, then (x - y) = ?











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    Given, 6x - 10y = 10 ..........(i)
    and x/(x + y) = 5/7
    ⇒ 7x = 5x + 5y
    ⇒ 2x - 5y = 0 ...(ii)

    Multiplying Eq. (ii) by 2 and subtracting from Ed.(i),

    Correct Option: D

    Given, 6x - 10y = 10 ..........(i)
    and x/(x + y) = 5/7
    ⇒ 7x = 5x + 5y
    ⇒ 2x - 5y = 0 ...(ii)

    On multiplying Eq. (ii) by 2 and subtracting from Ed.(i), we get
    6x - 10y = 10
    4x - 10y = 0
    ---------------------
    2x = 10
    ∴ x = 5
    Putting the value of x in Eq. (i), we get
    30 - 10y = 10
    ⇒ 10y = 20
    ⇒ y = 2
    ∴ (x - y) = 5 - 2 = 3


  1. The system of equations 2x + 4y = 6 and 4x + 8y = 6 has











  1. View Hint View Answer Discuss in Forum

    Given equations 2x + 4y = 6 and 4x + 8y = 6

    then,
    a1/a2 = 2/4 = 1/2;
    b1/b2 = 4/8 = 1/2;
    c1/c2 = 6/6 = 1
    ∴ a1/b2 = b1/b2 ≠ c1/c2

    Correct Option: B

    Given equations 2x + 4y = 6 and 4x + 8y = 6

    then,
    a1/a2 = 2/4 = 1/2;
    b1/b2 = 4/8 = 1/2;
    c1/c2 = 6/6 = 1
    ∴ a1/b2 = b1/b2 ≠ c1/c2

    So there is no solution for these equations.



  1. In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1 : 2, Based on the information; the total number of coins in the collection now becomes.









  1. View Hint View Answer Discuss in Forum

    Let the number of gold coins initially be x and the number of non-gold coins be y.
    According to the question,
    3x = y

    When 10 more gold coins, total number of gold coins becomes x + 10 and the number of non-gold coins remain the same at y.
    Now, we have 2(x + 10) = y

    Solving these two equations, we get
    x = 20 and y = 60.

    Correct Option: A

    Let the number of gold coins initially be x and the number of non-gold coins be y.
    According to the question,
    3x = y

    When 10 more gold coins, total number of gold coins becomes x + 10 and the number of non-gold coins remain the same at y.
    Now, we have 2(x + 10) = y

    Solving these two equations, we get
    x = 20 and y = 60.
    Total number of coins in the collection at the end is equal to
    x + 10 + y = 20 + 10 + 60 = 90.