Question

The ratio of two number is $3:8$ and their difference is 115. the larger number is:
(A) 69
(B) 115
(C) 184
(D) 230

Answer 1

Hint: Convert the word problem into mathematical equation. A number written in the form, $\dfrac{p}{q}$where $q \ne 0$is called fraction.

Complete Step by step solution:
Let $a$and $b$be the two required numbers.
Then, according to the first part of the question, we can write
$\dfrac{a}{b} = \dfrac{3}{8}$
Let $x$ be the common factor in the ratio.
Then the two number will be $a = 3x$and $b = 8x$ . . . (1)
It is given that the difference of two numbers is 115.
$ \Rightarrow 8x - 3x = 115$
Simplifying this equation, we get
$5x = 115$
$ \Rightarrow x = \dfrac{{115}}{5}$
$ \Rightarrow x = 23$
Put the value of$x$in equation (1)
$ \Rightarrow b = 8x = 8 \times 23$
$ \Rightarrow b = 184$
And
$a = 3x = 3 \times 23$
$ \Rightarrow a = 69$
By comparing the values of $a$and $b$we can conclude that the larger number is, $b = 184$

Additional information:
Ration helps us to compare two quantities with the same unit.
In the ratio $\dfrac{p}{q},q \ne 0$because, if $q = 0$then the fraction will not exist as the whole term will be infinity.
Every fraction is not necessarily a rational number. For example, $\dfrac{1}{2}$is a fraction as well as a rational number. $\dfrac{1}{{\sqrt 2 }}$ is a fraction but not a rational number.

Note: It is better to read the word problem in parts and convert every part into a mathematical equation before going ahead with the next part. It avoids confusion, helps to understand the question in a better way and saves time. Always, first convert the word problem into a mathematical equation and then think about the approach that you should use to solve the question.
Do not assume which one of $a$ or $b$ will be a larger number before getting the final answer. We wrote $8x - 5x = 115$without knowing if $8x$is a larger number or not. But it does not create any problem because if $5x$ would be a larger number, then the value of $x$ will be negative.