Question

If $a:b=2:5$, then find the sum of Numerator and Denominator for $(2a+3b):(7a+5b).$

Answer 1

We have,

$a:b=2:5$

$\frac{a}{b}=\frac{2}{5}$

Since,

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

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

$\Rightarrow \frac{2\times 2/5+3}{7\times 2/5+5}$

$\Rightarrow \frac{4/5+3}{14/5+5}$

$\Rightarrow \frac{4+15}{14+25}$

$\Rightarrow \frac{19}{39}$

So, the sum of numerator and denominator will be

$=19+39=58$

Hence, this is the answer.