Question

If $\frac{a}{3}=\frac{b}{2}$ then find the value of the ratio
$\frac{5a+3b}{7a-2b}$.

• A. $\frac{19}{17}$
• B. $\frac{21}{17}$
• C. $\frac{22}{17}$
• D. $\frac{20}{17}$

Answer 1

The correct option is B $\frac{21}{17}$

Given: $\frac{a}{3}=\frac{b}{2}$

$\therefore \frac{a}{b}=\frac{3}{2}....\left(\text{using Alternendo}\right)$

To calculate: $\frac{5a+3b}{7a-2b}$
Now dividing each term of $\frac{5a+3b}{7a-2b}$ by $b$.

$=\frac{\frac{5a}{b}+\frac{3b}{b}}{\frac{7a}{b}-\frac{2b}{b}}$

$=\frac{5\left(\frac{a}{b}\right)+3}{7\left(\frac{a}{b}\right)-2}$

On substituting the value of $\frac{a}{b}$;

$\Rightarrow =\frac{5\left(\frac{3}{2}\right)+3}{7\left(\frac{3}{2}\right)-2}$

$\Rightarrow =\frac{\frac{15}{2}+3}{\frac{21}{2}-2}$

$\Rightarrow =\frac{15+6}{21-4}$

​​​​​​​$\Rightarrow =\frac{21}{17}$