Question 42: Find x in the proportions \(\left( {{1 \over 3}x} \right):{2 \over 3} = 1{3 \over 4}:{2 \over 5}\ )

A. \(x= \dfrac{{31}}{4}\)

B. \(x= \dfrac{{39}}{4}\)

C. \(x= \dfrac{{37}}{4}\)

D. \(x= \dfrac{{35}}{4}\)

\(\left( {{1 \over 3}x} \right):{2 \over 3} = 1{3 \over 4}:{2 \over 5}\)

\(\Rightarrow \left( {\dfrac{1}{3}x} \right).\dfrac{2}{5} = \dfrac{2}{3}.1\dfrac{3}{4}\ )

\(\Rightarrow \dfrac{1}{3}x = \dfrac{{\dfrac{2}{3}.\dfrac{7}{4}}}{{\dfrac{2}{5}}}\ )

\(\Rightarrow \dfrac{1}{3}x = \dfrac{{35}}{{12}}\)

\(\Rightarrow x = \dfrac{{35}}{{12}}:\dfrac{1}{3} = \dfrac{{35}}{4}\)

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