Question

Simplify $ 78 - \left[ {5 + 3\left( {25 - 2 \times 10} \right)} \right] $
A.58
B.12
C.30
D.75

Answer 1

Hint: Here, we can see that we have to perform different types of operations to simplify the given problem. Therefore we need to use the BODMAS rule. In this rule, B stands for brackets, O stands for order, D stands for division, M stands for multiplication, A stands for addition and S stands for subtraction.
Formula used:
BODMAS rule:
B {Brackets): Simplify anything which is in the bracket first before Order, Multiply, Divide, Add or Subtract.
O (Order): Then, solve the Order part which may include powers or roots before Multiply, Divide, Add or Subtract.
D and M (Division and Multiplication): Then do any division or multiplication before Add or Subtract. If both are there in the same calculation, we can complete them from left to right.
A and S (Addition and Subtraction): The last step is to do addition or subtraction. If both are there in the same calculation, we can complete them from left to right.

Complete step-by-step answer:
 $ 78 - \left[ {5 + 3\left( {25 - 2 \times 10} \right)} \right] $
As per the BODMAS rule, we will first solve the bracket part $ \left( {25 - 2 \times 10} \right) $ . Again in this part, there are two operations: subtraction and multiplication. Therefore, we will multiply first and then subtract.
Simplify multiplication in the bracket
 $ \Rightarrow 78 - \left[ {5 + 3\left( {25 - 20} \right)} \right] $
Simplify subtraction in the bracket
 $ \Rightarrow 78 - \left[ {5 + 3\left( 5 \right)} \right] $
Now, if we open the bracket, it will be an operation of multiplication:
 $ \Rightarrow 78 - \left[ {5 + 3 \times 5} \right] $
Simplify the multiplication
  $ \Rightarrow 78 - \left[ {5 + 15} \right] $
Simplify addition
 $ \Rightarrow 78 - \left[ {20} \right] $
Open the bracket
 $ \Rightarrow 78 - 20 $
Finally, by subtracting, we get the answer,
 $ \Rightarrow 78 - 20 = 58 $
Thus, our final answer is $ 58 $ .
Hence, option A is the right answer.
So, the correct answer is “Option A”.

Note: The BODMAS rule helps us by an acronym to remember the proper order of mathematical operations. This is the correct and the proper order in which the mathematical calculations should be done. When there are different operations involved in a problem, applying BODMAs rules helps us to solve it in the correct order as we have done in this question.