Question

Two numbers are in the ratio 10:11. Their sum is 168. Find the numbers.

Answer 1

Hint: We will first consider the given ratio, that is 10:11. We will next consider that $x$ represents the common ratio, therefore as the two numbers are in the ratio 10:11, it implies that $10x$ and $11x$ are the two numbers. Now the sum of the two numbers is given as 168. So, we will form an equation and evaluate the value of $x$ from that equation and then substitute the value of $x$in the two numbers $10x$ and $11x$, which will give us our required answer.

Complete step-by-step solution:
We will first consider the ratio of the two numbers as $10:11$. The objective is to find the two numbers. Now, we will let that common ratio be shown by $x$. Hence two numbers are represented by $10x$ and $11x$respectively. So, we will form an equation using this, thus we get,
$\begin{align}
  & 10x+11x=168 \\
 & \Rightarrow 21x=168 \\
\end{align}$
Next, we will solve this for getting the value of $x$. So,
 $x=\dfrac{168}{21}=8$
Now we will find the values of the two numbers by substituting the value of $x$ in $10x$ and $11x$.
Hence the first number is $10x=10\times 8=80$.
And the second number is $11x=11\times 8=88$.
Thus the two numbers are 80 and 88.

Note:Form the equation properly after carefully reading the given statement. As the ratio is given, we can write the numbers in the terms of $x$, where $x$ shows the common ratio. Simplify the equation properly without doing any calculation mistakes. While substituting the value of $x$, do the calculations carefully.