Question

Find the sum of two numbers whose ratio is 7:19 and their difference is 12
A.22
B.26
C.24
D.23

Answer 1

Hint: In this question, we are given a mathematical statement, so we will first convert it into a mathematical equation using the given information. We are given the relation between two numbers and we have to find the two numbers using the given relations. We will let the two numbers to be represented by alphabets “x” and “y”, it is obvious that one of the two numbers will be greater than the other, from the ratio, we see “y” is greater than “x”. And we will get two equations because two relations are given to us. Solving the two equations, we will get the value of the two numbers and thus get their sum.

Complete step by step solution:
We are given that the ratio of the two numbers is 7:19, that is, x:y is 7:19, or we can also write is as –
 $
  \dfrac{x}{y} = \dfrac{7}{{19}} \\
   \Rightarrow x = \dfrac{{7y}}{{19}} \;
  $
From the above equation, we clearly see that x is smaller than y.
We are also given that the difference of these two numbers is 12, as “y” is greater than “x”, so we get –
 $ y - x = 12 $
On putting the value of “x” in the above equation, we get –
 $
  y - \dfrac{{7y}}{{19}} = 12 \\
   \Rightarrow \dfrac{{19y - 7y}}{{19}} = 12 \\
   \Rightarrow \dfrac{{12y}}{{19}} = 12 \\
   \Rightarrow y = 12 \times \dfrac{{19}}{{12}} \\
   \Rightarrow y = 19 \;
  $
We get –
 $
  x = \dfrac{{7 \times 19}}{{19}} \\
   \Rightarrow x = 7 \;
  $
So, we get $ x = 7 $ and $ y = 19 $ .
 $
  x + y = 7 + 19 \\
   \Rightarrow x + y = 26 \;
  $
So the sum of the two numbers is 26.
Hence option (B) is the correct answer.
So, the correct answer is “Option B”.

Note: The mathematical equation containing a combination of alphabets and numerical values is known as an algebraic expression. In algebraic expressions, the alphabets representing the unknown variable quantity are related to the numerical values by some arithmetic operations, and to find the value of “n” unknown quantities, we need “n” number of equations.