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    If A : B = 3 : 7 and B : C = 2 : 5, find A : B : C.
    Question

    If A : B = 3 : 7 and B : C = 2 : 5, find A : B : C.

    A.

    10 : 3 : 4

    B.

    4 : 10 : 3

    C.

    4 : 3 : 10

    D.

    6 : 14 : 35

    Correct option is D

    Given:
    A : B = 3 : 7
    B : C = 2 : 5,
    Solution:​​
    AB=37(i)BC=25(ii)Multiplying by 2 in (i) and by 7 in (ii) to make B the same in both ratios:AB=3×27×2=614BC=2×75×7=1435\frac{A}{B} = \frac{3}{7} \quad \text{……(i)}\\\frac{B}{C} = \frac{2}{5} \quad \text{……(ii)}\\\text{Multiplying by 2 in (i) and by 7 in (ii) to make B the same in both ratios:}\\\frac{A}{B} = \frac{3 \times 2}{7 \times 2} = \frac{6}{14}\\\frac{B}{C} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}\\​​
    Therefore,
    A : B : C = 6 : 14 : 35
    Alternate Method:

    ABC37722561435\begin{array}{c|c|c}A & B & C \\\hline3 & 7 & 7 \\2 & 2 & 5 \\\hline6 & 14 & 35\end{array}

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