Question

If $a:b=3:5,\text{find:}(10a+3b):(5a+2b)$

Answer 1

Step: Find $(10a+3b):(5a+2b)$

Divide numberator and denominator both by b

$\frac{10a+3b}{5a+2b}=\frac{\frac{10a+3b}{b}}{\frac{5a+2b}{b}}$

$=\frac{10\frac{a}{b}+3}{5\frac{a}{b}+2}$

$=\frac{10\times \frac{3}{5}+3}{5\times \frac{3}{5}+2}$ $[\therefore \frac{a}{b}=\frac{3}{5}]$

$=\frac{(2\times 3)+3}{3+2}$

$=\frac{9}{5}$

Hence, the value of $(10a+3b):(5a+2b)\text{is}9:5.$