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Difficulty: HardSimplification and BODMAS Rule
What is the simplified value of the following expression?
25% of 160−[12÷{315+(1.8−0.6+0.4‾)}]×525\% \text{ of } 160 - \left[ 12 \div \left\{ 3\frac{1}{5} + \left( 1.8 - \overline{0.6 + 0.4} \right) \right\} \right] \times 5
  1. 25Answer
  2. B
    185
  3. C
    27.5
  4. D
    39.4

Answer

25
Evaluating the expression following the standard BODMAS priority (Vinculum →\rightarrow Brackets →\rightarrow Orders/Percentage →\rightarrow Division →\rightarrow Multiplication →\rightarrow Subtraction):
1. Vinculum: 0.6+0.4‾=1\overline{0.6 + 0.4} = 1
2. Round brackets: 1.8−1=0.81.8 - 1 = 0.8
3. Curly brackets: 315+0.8=3.2+0.8=43\frac{1}{5} + 0.8 = 3.2 + 0.8 = 4
4. Square brackets: 12÷4=312 \div 4 = 3
5. Percentage: 25% of 160=4025\% \text{ of } 160 = 40
6. Final calculation: 40−(3×5)=40−15=2540 - (3 \times 5) = 40 - 15 = 25.
Hence, the correct value is 25.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar 0.6+0.4‾\overline{0.6 + 0.4}
0.6+0.4=1.00.6 + 0.4 = 1.0
The vinculum (bar bracket) takes the highest priority in the hierarchy of brackets.
2
Evaluate the innermost round brackets (1.8−1.0)(1.8 - 1.0)
1.8−1.0=0.81.8 - 1.0 = 0.8
Round brackets must be resolved next after the vinculum.
3
Convert mixed fraction 3153\frac{1}{5} to decimal and evaluate the curly brackets {3.2+0.8}\left\{ 3.2 + 0.8 \right\}
315=3.23\frac{1}{5} = 3.2, so 3.2+0.8=4.03.2 + 0.8 = 4.0
Curly brackets are evaluated after resolving all inner terms.
4
Evaluate the square brackets [12÷4.0]\left[ 12 \div 4.0 \right]
12÷4=312 \div 4 = 3
Square brackets enclose the remaining multi-bracket expression.
5
Evaluate the 'of' percentage operation 25% of 16025\% \text{ of } 160
25100×160=40\frac{25}{100} \times 160 = 40
'Of' / percentage operations take precedence over standard multiplication and subtraction.
6
Perform multiplication before subtraction in 40−3×540 - 3 \times 5
3×5=153 \times 5 = 15, then 40−15=2540 - 15 = 25
According to BODMAS, multiplication precedes subtraction.

Key Concept

Hierarchy of Brackets and BODMAS Rule
Estimated Time:2m 0s
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Topics

Simplification and BODMAS Rule

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