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    If a : b :: 3 : 4 then the value of expression 5a−3b7a+2b\frac{5a-3b}{7a + 2b} 7a+2b5a−3b​ is :​
    Question

    If a : b :: 3 : 4 then the value of expression 5a3b7a+2b\frac{5a-3b}{7a + 2b}  is :​

    A.

    329\frac{3}{29} ​​

    B.

    293\frac{29}{3} ​​

    C.

    729\frac{7}{29} ​​

    D.

    73\frac{7}{3} ​​

    Correct option is A

    Given:

    a:b=3:4a : b = 3 : 4​​

    Solution:

    Let a=3ka = 3k​ and b=4kb = 4k​ (where k is a constant).

    Expression: 5a3b7a+2b\frac{5a - 3b}{7a + 2b}​​

    Substituting values of  a and b; 

    5(3k)3(4k)7(3k)+2(4k)\frac{5(3k) - 3(4k)}{7(3k) + 2(4k)}=15k12k21k+8k= \frac{15k - 12k}{21k + 8k}​  =3k29k=329= \frac{3k}{29k}=\frac{3}{29}​​


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