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10th Class Mathematics Related to Competitive Exam Question Bank Commercial Mathematics

  • question_answer
    Let A : (B + C) = 6 : 7 and B : (A + C) = 8 : 9. If a sum of Rs. 221 is divided among A, B, C, then the shares of A, B, C (in Rs.) respectively will be

    A)  102, 104, 15       

    B)         100,106,15

    C)  104,100,17      

    D)         80,100,41

    Correct Answer: A

    Solution :

     By hypothesis,  \[\frac{A}{B+C}=\frac{6}{7}\] or            \[7A=6(B+C)\] or            \[7A-6B-6C=0\] ??(i) and        \[\frac{B}{A+C}=\frac{8}{9}\] or            \[9B=8(A+C)\] or            \[8A-9B+8C=0\]                ?..(ii) Solving equations (i) and (ii) by cross multiplication, we get \[\frac{A}{-48-54}=\frac{b}{-48-56}=\frac{C}{-63+48}\]                 or            \[\frac{A}{-102}=\frac{B}{-104}=\frac{C}{-15}\]                 or            \[\frac{A}{102}=\frac{B}{104}=\frac{C}{15}\] \[\therefore \]Sum of ratios \[=102+104+15=221\] Hence, A, B and C's shares are respectively \[Rs.102,\text{ }Rs.\text{ }104\] and \[Rs.\text{ }15\].


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