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    Three numbers are in the ratio 514:1613:2014\frac{5}{14} : \frac{16}{13} : \frac{20}{14}145​:1316​:1420​. The difference between the largest and
    Question

    Three numbers are in the ratio 514:1613:2014\frac{5}{14} : \frac{16}{13} : \frac{20}{14}. The difference between the largest and the smallest number is 30. Find the largest number.

    A.

    40

    B.

    39

    C.

    41

    D.

    42

    Correct option is A

    Given: 

    514:1613:2014\frac{5}{14} : \frac{16}{13} : \frac{20}{14} 

    Largest number - smallest number = 30 

    Solution: 

    514:1613:2014 =65:224:260\frac{5}{14} : \frac{16}{13} : \frac{20}{14} \\ \ \\ = 65 : 224 : 260 

    Now, 

    260x - 65x = 30

    195x = 30 

    x = 30195=213\frac{30}{195} = \frac2{13} 

    So, Largest number = 213×260=40\frac2{13}\times 260 = 40​​

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