Question : If $A=\frac{2}{3}+\frac{4}{7}$ of $\frac{14}{12}$ and $B=\frac{5}{12}$ of $\frac{7}{15} \times \frac{36}{21}$, then what is the value of $A + B$?
Option 1: $\frac{5}{3}$
Option 2: $2$
Option 3: $\frac{4}{3}$
Option 4: $\frac{2}{3}$
Correct Answer: $\frac{5}{3}$
Solution :
$A=\frac{2}{3}+\frac{4}{7}$ of $\frac{14}{12}$
$=\frac{2}{3}+\frac{4}{7}\times\frac{14}{12}$
$=\frac{4}{3}$
$B=\frac{5}{12}$ of $\frac{7}{15} \times \frac{36}{21}$
$=\frac{5}{12}\times\frac{7}{15} \times \frac{36}{21}$
$=\frac{1}{3}$
$⇒ A + B =\frac{4}{3}+\frac{1}{3}= \frac{5}{3}$
Hence, the correct answer is $\frac{5}{3}$.
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