Question

If a is greater than b by 2 and b is greater than c by 10 and a + b + c = 130, then (b + c) – a = ?
(a) 34
(b) 42
(c) 38
(d) 44

Answer 1

Hint: As all the variables given in the question are of the form of a, b and c and they are all related to each other, then we will first make a relation between all of them using any one of a, band c. Finally using the condition a + b + c = 130. We can determine the value of a variable and hence the given condition can be determined easily.

Complete step-by-step answer:
Given that a is greater than b by 2.
Converting this into equation form we get,
a = b + 2 – (1)
Again it is given that b is greater than c by 10 connecting this to equation form we get,
b = c + 10 – (2)
Comparing equation (1) and (2), we have,
a = b + 2
Using (2) gives,
\[\begin{align}
  & \Rightarrow a=\left( c+10 \right)+2 \\
 & \Rightarrow a=c+12 \\
\end{align}\]
So, we have three numbers a, b and c as,
\[\begin{align}
  & a=c+12 \\
 & b=c+10 \\
\end{align}\]
And c,
Also we are given that, a + b + c = 130 – (3)
Substituting the value of a, b and c obtained above in equation (3), we get;
\[\begin{align}
  & \Rightarrow a+b+c=130 \\
 & \Rightarrow c+12+c+10+c=130 \\
 & \Rightarrow 3c+22=130 \\
 & \Rightarrow 3c=130-22 \\
 & \Rightarrow c=\dfrac{108}{2} \\
 & \Rightarrow c=36 \\
\end{align}\]
So, the value of a = c + 12 = 36 + 12 = 48.
And value of b = c + 10 = 36 + 10 = 46.
And c = 36.
Now the last step is to determine the value of (b + c) – a.
\[\begin{align}
  & \Rightarrow \left( 46+36 \right)-48 \\
 & \Rightarrow 82-48 \\
 & \Rightarrow 34 \\
\end{align}\]
So, the value of \[\left( b+c \right)-a=34\],
So, the correct answer is “Option A”.

Note: The possibility of error in this question can be not determining the value of variables a and b and c and directly proceeding to determine value of (b + c) – a. This will lead to a variable arriving at the answer part which would be wrong as we need numerical value as answer.