Question

Find a number which has the same ratio to $ 32 $ as $ 18 $ has to $ 24 $

Answer 1

Hint: Ratio can be defined as the comparison between two numbers without any units. Whereas, when two ratios are set equal to each other are known as the proportion. Four numbers a, b, c, and d are supposed to be in proportion. If $ a:b = c:d $ . Here, we will assume the unknown term “x” which has the same ratio to the given terms.

Complete step by step solution:
Let us assume that number be “x” which has the same ratio to $ 32 $ as $ 18 $ has to $ 24 $
“x” has the same ratio to $ 32 $
The above statement is expressed as - $ \dfrac{x}{{32}} $ ….. (A)
ratio $ 18 $ has to $ 24 $ is expressed as- $ \dfrac{{18}}{{24}} $ ….. (B)
Given that both the terms follow the same ratios.
 $ \dfrac{x}{{32}} = \dfrac{{18}}{{24}} $
Simplify the above expression, performing the cross multiplication where the numerator of one side is multiplied with the denominator of the other side and vice-versa and make the required term “x” the subject -
 $ x = \dfrac{{18 \times 32}}{{24}} $
Find the factors of the terms in the above expression –
 $ x = \dfrac{{6 \times 3 \times 8 \times 4}}{{6 \times 4}} $
Common factors from the numerator and the denominator cancel each other.
 $ x = 3 \times 8 $
Simplify the above expression finding the product of the terms.
 $ x = 24 $
So, the correct answer is “ $ x = 24 $ ”.

Note: Always read the question twice and frame the word statement in the mathematical form. Segregate all the known and unknown terms and form the corresponding ratios and the proportions accordingly. The above example can be solved in other alternative methods.
Let us assume that number be “x” which has the same ratio to $ 32 $ as $ 18 $ has to $ 24 $
 $ \dfrac{x}{{32}} = \dfrac{{18}}{{24}} $ and simplify for the value of “x”.