Question

The difference between two numbers is $ 8 $ and their ratio is $ 1:5. $ Which of the following is the smaller number?
A. $ 24 $
B. $ 8 $
C. $ 10 $
D. $ 2 $

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 called the proportion. Here we will assume the unknown number to be “x” and will frame mathematical expressions and will simplify for the resultant value.

Complete step-by-step answer:
Let us assume the unknown number be “x”
Here, we are given that the ratios of the two numbers are $ 1:5. $
It can be expressed as $ \dfrac{1}{5} = \dfrac{{1x}}{{5x}} $
Also given that the difference of two numbers is $ 8 $
 $ \therefore 5x - x = 8 $
Simplify the above expression finding the difference of the terms –
 $ 4x = 8 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ x = \dfrac{8}{4} $
Find the factors for the term in the numerator.
 $ x = \dfrac{{4 \times 2}}{4} $
Common factors from the numerator and the denominator cancels each other and therefore remove
 $ x = 2 $
Hence the smaller number is $ 2 $
Hence, from the given multiple choices – the option D is the correct answer.
So, the correct answer is “Option D”.

Note: Always read the question twice and frame the word statement in the correct mathematical form. Segregate all the known and unknown terms and form the corresponding correlation between the two terms. Know the concepts of ratios and proportion and apply accordingly. Four numbers a, b, c, and d are called to be in the proportion. If $ a:b = c:d $ whereas, four numbers are known as in continued proportion if the terms $ a:b = b:c = c:d $