What is the numerical value of the mathematical expression given below when evaluated stri… — State PSC Exam

What is the numerical value of the mathematical expression given below when evaluated strictly according to the VBODMAS rule?

18\% \text{ of } 250 + \left[ 34 - \left\{ 12 \times 2.5 - \left( 14 \div 2 + \overline{8 - 3} \right) \right\} \right]

Following the VBODMAS priority rule, we first clear the vinculum

\overline{8-3}=5

. Next, within the round brackets, division precedes addition:

14 \div 2 + 5 = 7 + 5 = 12

. Inside the curly brackets, multiplication precedes subtraction:

12 \times 2.5 - 12 = 30 - 12 = 18

. The square bracket reduces to

34 - 18 = 16

. Evaluating

18\%

250

gives

45

. Adding

45 + 16

yields the correct final result of 61.

Evaluate the vinculum bar term

\overline{8 - 3} = 5

According to VBODMAS, operations under a vinculum (bar) must be simplified first.

Simplify the innermost round brackets

(14 \div 2 + 5) = 7 + 5 = 12

Division takes precedence over addition inside the parentheses.

Simplify the curly brackets

\{ 12 \times 2.5 - 12 \} = 30 - 12 = 18

Multiplication is performed before subtraction inside the brace group.

Simplify the square brackets

[ 34 - 18 ] = 16

Complete the bracket hierarchy by evaluating the outer square brackets.

Evaluate the 'of' percentage term

18\% \text{ of } 250 = \frac{18}{100} \times 250 = 45

The percentage 'of' operator is calculated as multiplication.

Perform the final addition

45 + 16 = 61

Combine the percentage term with the simplified bracket result.

VBODMAS Rule (Vinculum, Brackets, Of, Division, Multiplication, Addition, Subtraction)

Question