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7th Class Mathematics Comparing Quantities Question Bank Comparing Quantities

  • question_answer
    The ratio of the length of Rope A to the length of Rope B is\[3:4\]. The ratio of the length of Rope C to the length of Rope B is \[7:6\]. If the length of the longest rope is 84 cm, find the total length of the three ropes.

    A)  210 cm          

    B)  225 cm          

    C)         185 cm       

    D)         200 cm

    Correct Answer: A

    Solution :

    Let the length of Rope A be 3x and length of Rope 8 be 4x. Given that. \[\frac{Length\,\,of\,\,Rope\ C}{Length\,\,of\,\,Rope\,B}=\frac{7}{6}\] \[\Rightarrow \] Length of Rope C \[=\frac{7}{6}\times \] Length of Rope \[B=\frac{7}{6}\times 4x=\frac{14x}{3}\] \[\therefore \]  Rope C is the longest rope. \[\Rightarrow \]  \[\frac{14x}{3}=84\Rightarrow x=18\] \[\therefore \] Length of Rope \[A=3\times 18=54cm\] Length of Rope \[~B=4\times 18=72cm\] Hence, total length of three ropes \[=84+54+72=210\text{ }cm\]


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