Question

If we have the ratio such as (3a+2b):(5a+3b)=18:29. Then find a:b.

Answer 1

Hint: Think of the basic definition of ratio and use the fractional form of a ratio. Then solve the equation you get, by using the fractional form of the ratio to express a in terms of b.

Complete step-by-step solution -
Let us first know what a ratio is.
A ratio in basic words is a quantity used to define a comparison between two quantities. A bit toward the advanced side, it is the quantity that defines how many times of one quantity is that of others.
 At our level, apart from the definition, we will treat it as a simple fraction that defines a relation between two given quantities.
Now, starting with the solution to the above question. First, we will convert the ratio given in the question to the fractional form. On doing so, we get
$\dfrac{3a+2b}{5a+3b}=\dfrac{18}{29}$
Now to further solve the equation, we will cross-multiply. On doing so, we get
$29\left( 3a+2b \right)=18\left( 5a+3b \right)$
Now if we multiply and open the brackets, we get
$87a+58b=90a+54b$
$\Rightarrow 3a=4b$
$\Rightarrow \dfrac{a}{b}=\dfrac{4}{3}$
Therefore, the ratio a:b is 4:3.

Note: Read the question carefully as in the question, including ratio, there is always a chance that the question might have a twist hidden in the words of the question. Also, while solving a fraction for finding the ratio, be sure that you convert it to the simplest form, i.e., the numerator and the denominator must not have any common factors.