Question

What is the ratio whose terms differ by 40 and the measure of which is $\dfrac{2}{7}$?
A). 16: 56
B). 14: 56
C). 15: 56
D). 16: 72

Answer 1

Hint: First we will let the two terms whose ratio we have to find as x and y. Then, some conditions are given in the question like one term differs by 40 from other terms and the measure of both the terms is $\dfrac{2}{7}$. We will use these to find the answer.

Complete step-by-step solution:
Let the first term be x.
Let the second term be y.
It is given that the terms differ by 40. So, we can take the second term as 40 more than the first term.
$y = x + 40$
It is also given that the measure of both the terms is $\dfrac{2}{7}$. So,
$\dfrac{x}{{x + 40}} = \dfrac{2}{7}$
$\Rightarrow 7x = 2x + 80$
$\Rightarrow 7x - 2x = 80$
$\Rightarrow 5x = 80$
$\Rightarrow x = \dfrac{{80}}{5}$
$\Rightarrow x = 16$
The value of the first term is equal to 16.
Second term = $x + 40$
$ = 16 + 40$
$ = 56$
So, the value of the second term is 56.
The ratio of these two terms is 16: 56.
So, option (1) is the correct answer.

Note: The ratio is the number which can be used to express one quantity as a fraction of the other ones. The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things.
In this case, we took the second term as 40 more than the first term (y = x+40). We can also take it as the first term is 40 more than the second term (x = y+40) and also as the second term is 40 less than the first term (y = x-40). The answer will be the same in all cases.