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Difficulty: MediumSimplification and BODMAS Rule
What is the simplified numerical value of the mathematical expression given below when evaluated strictly according to the VBODMAS rule?
15% of 200−[36÷{18−(2×7−4‾)}]×3.515\% \text{ of } 200 - \left[ 36 \div \left\{ 18 - \left( 2 \times \overline{7 - 4} \right) \right\} \right] \times 3.5
  1. 19.519.5Answer
  2. B
    94.594.5
  3. C
    14.2514.25
  4. D
    27.527.5

Answer

The simplified numerical value of the expression is 19.519.5.
Following the VBODMAS hierarchy, we first solve the bar term 7−4‾=3\overline{7-4} = 3, giving (2×3)=6(2 \times 3) = 6 inside the inner bracket. Next, the curly bracket simplifies to 18−6=1218 - 6 = 12. The square bracket simplifies to 36÷12=336 \div 12 = 3. Evaluating 15% of 200=3015\% \text{ of } 200 = 30 and the product 3×3.5=10.53 \times 3.5 = 10.5, we get 30−10.5=19.530 - 10.5 = 19.5.

Step-by-Step Solution

1
Evaluate the expression under the Vinculum (bar)
7−4‾=3\overline{7 - 4} = 3
According to VBODMAS, operations under the vinculum have the highest priority.
2
Evaluate the innermost round bracket ()( )
2×3=62 \times 3 = 6
Resolve the multiplication inside the round brackets.
3
Evaluate the curly bracket {}\{ \}
18−6=1218 - 6 = 12
Perform subtraction inside the curly brackets.
4
Evaluate the square bracket [][ ]
36÷12=336 \div 12 = 3
Perform division inside the square brackets.
5
Calculate the percentage portion
15% of 200=15100×200=3015\% \text{ of } 200 = \frac{15}{100} \times 200 = 30
'Of' represents multiplication in percentage evaluation.
6
Perform multiplication before final subtraction
3×3.5=10.53 \times 3.5 = 10.5
Multiplication takes precedence over final subtraction.
7
Perform final subtraction
30−10.5=19.530 - 10.5 = 19.5
Subtract the result of the bracketed expression term from the percentage term.

Key Concept

Order of Operations (VBODMAS Rule)
Estimated Time:1m 30s
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Topics

Simplification and BODMAS Rule

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