Question

If $A$ stands for $+$, $B$ stands for $ - $, $C$ stands for $ \times $ and $D$ stands for $ \div $ then what is the value of $\left( {10\,C\,4} \right)A\left( {4\,C\,4} \right)B\,6$ ?
A. $46$
B. $50$
C. $56$
D. $60$

Answer 1

Hint: In this question each variable is assigned a different operation and we have to find the value of the given expression using them. Firstly we will simplify the statement by substituting the operation symbol in place of the variables and make it an arithmetic expression. Then we will use the BODMAS rule to solve our obtained arithmetic expression to get the desired answer.

Complete step-by-step solution:
It is given to us that
$A$ Stands for $ + $ $ \Rightarrow A = + $
$B$ Stands for $ - $ $ \Rightarrow B = - $
$C$ Stands for $ \times $ $ \Rightarrow C = \times $
$D$ Stands for $ \div $ $ \Rightarrow D = \div $
We have to find the value of the given expression:
 $\left( {10\,C\,4} \right)A\left( {4\,C\,4} \right)B\,6$
On substituting the value of all the variables in above expression we get,
$\left( {10 \times 4} \right) + \left( {4 \times 4} \right) - 6$
Now using BODMAS we will solve the bracket values first as follows:
$ \Rightarrow \left( {40} \right) + \left( {16} \right) - 6$
Next we will solve the terms with addition operation followed by subtracting as follows:
$ = 56 - 6$
$ = 50$
So we get the value of $\left( {10\,C\,4} \right)A\left( {4\,C\,4} \right)B\,6$ as $50$
Hence the correct option is (B).

Note: In this type of question we have to be careful while substituting the operation in place of variables as it is the most crucial step. Then we have to keep the BODMAS rule in mind for solving such questions as if the question is too complicated we can end up making mistakes in the calculation part. BODMAS is an acronym which stands for Brackets, Order (that means variables with power and roots etc.), Division, Multiplication, Addition and Subtraction. It is used to solve any arithmetic expression that involves multiple operations and brackets. In arithmetic an expression or equation involves two components i.e. Numbers and Operators.