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10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

  • question_answer
    The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs 2000 per month, then find their monthly incomes. Form a pair of linear equations from the above data and by elimination method, the value of monthly incomes are

    A) 18000, 14000

    B) 20000,12000

    C) 22000,10000

    D) None of the above

    Correct Answer: A

    Solution :

    Given, ratio of incomes \[=9:7\]
    and ratio of their expenditures \[=\text{ }4:3\]
    Saving of each person = Rs 2000
    Let incomes of two persons be 9 x, 7x and
    their expenditures be 4y, 3y.
    Then, linear equations so formed are
    \[9x-4y=2000\]              … (i)
    And \[7x-3y=2000\]
    We make the coefficients of x numerically equal in both equations. On multiplying
    Eq.(i) by 7 and Eq. (ii) by 9, we get
    \[63x-28y=14000\]         ...(iii)
    and       \[63x-27y=18000\]       ...(iv)
    On subtracting Eq. (iv) from Eq. (iii), we get
    \[-28y+27y=14000-18000\]
    \[\Rightarrow \,\,\,\,\,-y=-4000\,\,\,\,\Rightarrow \,y=4000\]
    On putting y = 4000 in Eq. (i), we get
    \[9x-4\times 4000=2000\]
    \[\Rightarrow \,\,\,\,\,9x=2000+16000\]
    \[\Rightarrow \,\,\,x=\frac{18000}{9}=2000\]
    Thus, monthly income of both persons are
    9(2000) and 7(2000), i.e. Rs 18000 and Rs 14000, respectively.


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