Question

Find a : b if (3a+b): (a + b) = 9:5.​

Answer 1

The given expression is $(3a+b): (a+b)=9:5$

We have to find $a:b$

$\frac{3a+b}{a+b} =\frac{9}{5}$

Taking cross multiplying , we get

$5(3a+b)=9(a+b)$

after that multiplying $5$ by $3a+b$ and $9$ by $a+b$

we get, $15a+5b=9a+9b$

shifting $5b$ to the right side it become minus and $9b$ to left side it become minus , we get

$15 a-9a=9b-5b$

         $6a=4b$

           $\frac{a}{b} =\frac{4}{6}$

           $\frac{a}{b} =\frac{2}{3}$

Therefore, the ratio of a:b is equal to $2:3$

Answer 2

To find : $a : b$

Given : $(3a+b): (a + b) = 9:5$

Solution :

• As per given data we have $(3a+b): (a + b) = 9:5$  .
• We can write above data as ,
• $\frac{3a + b}{a + b} = \frac{9}{5}$

       $15a + 5b= 9a +9b \\15 a -9a = 9b -5b \\6a = 4b \\\frac{a}{b} = \frac{4}{6} \\\frac{a}{b} = \frac{2}{3}$

    ⇒  $a: b= 2 : 3$  

Hence , ratio of  $a : b$ is $2 : 3$ .