Question

The sum of three numbers is 855. One of the numbers is x and is 50% more than the sum of the other two numbers. What is the value of x?
A. 570
B. 513
C. 214
D. 155

Answer 1

Hint:In order to solve this question, we will first consider three numbers as x, y and z and then, by using the given relations, we will try to express y + z in terms of x and we will form an equation to get the value of x for the answer.

Complete step-by-step answer:
In this question, we have been given that the sum of three numbers is 855 and out of those three numbers, one is x and that x and is 50% more than the sum of the other two numbers. And we have been asked to find the value of x. Let us consider the other two numbers as y and z. So, we can express the sum of y and z as y + z. Now, according to the question, we have been given that the sum of the three numbers is 855. So, we can write it as,
$x+y+z=855\ldots \ldots \ldots \left( i \right)$
Now, it is given that x is 50% more than the sum of the other two numbers. So, we can express x as,
$x=\left( y+z \right)+50\%\left( y+z \right)$
Now, we will simplify it further to get the value of y +z in terms of x. So, we can write,
$x=\left( y+z \right)+\dfrac{50}{100}\left( y+z \right)$
Now, we can take (y + z) common from right side of the equality. So, we get,
$\begin{aligned} & x=\left( y+z \right)\left( 1+\dfrac{50}{100} \right) \\\ & \Rightarrow x=\left( y+z \right)\left( 1+\dfrac{1}{2} \right) \\\ & \Rightarrow x=\left( y+z \right)\dfrac{3}{2} \\\ & \Rightarrow y+z=\dfrac{2x}{3}\ldots \ldots \ldots \left( ii \right) \\\ \end{aligned}$
From equation (ii), we will put the values of y + z in equation (i). So, we will get,
$x+\dfrac{2x}{3}=855$
Now, we will simplify it to get the value of x, which is the desired answer. So, we get,
$\begin{aligned} & \dfrac{3x+2x}{3}=855 \\\ & \Rightarrow \dfrac{5x}{3}=855 \\\ & \Rightarrow x=\dfrac{855\times 3}{5} \\\ & \Rightarrow x=171\times 3 \\\ & \Rightarrow x=513 \\\ \end{aligned}$
Hence, we get the value of x as 513. Therefore, option B is the correct answer.

Note: As we can see, in the question, we are always talking about the sum of the other two numbers. So, if we consider y as the sum of the other two numbers, instead of considering y and z as the other two numbers, we will get the same answer with lesser number of variables and less possibilities of calculation mistakes.