Question

Two numbers are in the ratio $8:3$. If the sum of the numbers is $143$, find the numbers.
(A) $14\,,39$
(B) $104\,,40$
(C) $10\,,39$
(D) $104\,,39$

Answer 1

Hint: Here we have to find two unknown numbers whose only ratio is known to us. Suppose the ratio be \[x\] then write both the numbers in terms of $x$ and then add both the numbers and equate the sum with the given sum of the numbers which give the required value of $x$. Finally, by putting the value of $x$ we get both the numbers.

Complete step-by-step answer:
Given, the two numbers are in the ratio $8:3$.
Let the ratio be $x$.
Then, the first number $ = 8x$
Second number $ = 3x$
Now, the sum of the two numbers $ = 8x + 3x = 11x$
It is given that the sum of the two numbers is $143$.
So, by equating the obtained sum of the two numbers with the given sum. We get,
$
   \Rightarrow 11x = 143 \\
   \Rightarrow x = \dfrac{{143}}{{11}} \\
  \therefore x = 13 \\
 $
Thus, the first number $ = 8 \times 13 = 104$
Second number $ = 3 \times 13 = 39$

Hence, option (D) is the correct option for this question.

Note: Similar concept is applied if the ratio of the numbers and the sum of two or more than two numbers is given. We have to add all the numbers written in terms of $x$ and then equate the sum with the given sum and then repeat the same as shown above.
If the ratio of the numbers is given and either their difference or product is given then a similar concept is applied but only difference is that in spite of addition of numbers we have to find the required i.e product or difference then repeat the same step as shown above.