Question

When a number is added to another number, the total becomes \[333\dfrac{1}{3}\] percent of the second number. What is the ratio between the first number and second number?
A. \[3:7\]
B. \[7:4\]
C. \[7:3\]
D. \[4:7\]

Answer 1

Hint: As we know the sum is result of adding two or more numbers and hence in the given question a number is added to another number implies that there are two terms and here to find the ratio of two unknown terms, consider any two random variables and form the equations as per the given statements in the question.

Complete step-by-step solution:
 For any given unknown number in the question, we need to consider any random variables for the unknown term.
As mentioned in the question a number when added to another number the total is
\[333\dfrac{1}{3}\]
For this let us consider \[x\] and\[y\] are the two numbers hence, when added the total becomes
\[333\dfrac{1}{3}\% \] of second number i.e., \[y\]
Hence as per the statement the equation is
\[x + y = 333\dfrac{1}{3}\% \] of \[y\]
After arranging the terms, we get
\[x + y = \dfrac{{1000}}{{3 \times 100}}y\]
\[x + y = \dfrac{{1000}}{{300}}y\]
Then after simplifying the terms we get
\[x + y = \dfrac{{10}}{3}y\]
Let us first solve for \[x\] term by combining the variables we get
\[x = \dfrac{{10}}{3}y - y\]
Taking \[y\]as a common term we get the below form
\[x = y\left( {\dfrac{{10}}{3} - 1} \right)\]
Hence the value of \[x\] as per the combined terms we get,
\[x = \dfrac{7}{3}y\]
The ratio between first number \[x\] and second number\[y\]is \[x = 7\] and \[y = 3\].
Hence in ratio form \[x\] and \[y\] are represented as
 \[x:y = 7:3\]

Therefore, the correct answer is option ‘C’.

Note: To find any values for these types of statements we need to consider any random variables as the unknown number, next solving as per the statements stated we can find out the values of any number asked. If they asked to find three numbers then consider \[x,y,z\]as the unknown variables and solve the sum.