• # question_answer If A : B = 2 : 3, B : C = 4: 5 and C : D = 6 : 7, then A : D = _____. A) 2 : 7                 B)          16 : 35       C) 4 : 13               D)          7 : 8

Solution :

$\frac{A}{B}=\frac{2}{3},\,\frac{B}{C}=\frac{4}{5},\,\frac{C}{D}=\frac{6}{7}$ From 2nd and 3rd expression we have $A=\frac{2}{3}\,B,\,B=\frac{4}{5},\,C=\frac{6}{7}D$ $B=\frac{4}{5}\times \frac{6}{7}D$ $A=\frac{2}{3}\times \,\frac{4}{5}\times \frac{6}{7}D$ $\frac{A}{D}=\frac{2}{\bcancel{3}}\times \frac{4}{5}\,\times \frac{{{\bcancel{6}}^{2}}}{7}=\frac{16}{35}$

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