If ‘A’ denotes ‘+’, ‘B’ denotes ‘×’, ‘C’ denotes ‘–’ and ‘D’ denotes ‘÷’, then what will come in place of ‘?’ in the following equation? 21 A 34 C 6 B (72 D 9) A 13 B 1 + (56 D 4) = ?
34
Decoding the Symbol Equation: A Step-by-Step Solution
The question asks us to evaluate a mathematical expression where specific letters represent arithmetic operators. We are given the following mapping:
- ‘A’ denotes ‘+’ (Addition)
- ‘B’ denotes ‘×’ (Multiplication)
- ‘C’ denotes ‘–’ (Subtraction)
- ‘D’ denotes ‘÷’ (Division)
The given expression is:
21 A 34 C 6 B (72 D 9) A 13 B 1 + (56 D 4) = ?
Step 1: Substitute the Symbols with Operators
Replace each letter in the expression with its corresponding mathematical operator:
21 + 34 – 6 × (72 ÷ 9) + 13 × 1 + (56 ÷ 4) = ?
Now we have a standard mathematical expression to evaluate.
Step 2: Apply the Order of Operations (BODMAS/PEMDAS)
We follow the standard order of operations:
- Brackets (or Parentheses)
- Orders (or Exponents)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Step 2a: Evaluate Expressions within Brackets
First, calculate the values inside the parentheses:
- $(72 \div 9) = 8$
- $(56 \div 4) = 14$
Substitute these values back into the expression:
21 + 34 – 6 × 8 + 13 × 1 + 14 = ?
Step 2b: Perform Multiplication and Division
Next, perform all multiplication and division operations from left to right:
- $6 \times 8 = 48$
- $13 \times 1 = 13$
Substitute these values back into the expression:
21 + 34 – 48 + 13 + 14 = ?
Step 2c: Perform Addition and Subtraction
Finally, perform all addition and subtraction operations from left to right:
- $21 + 34 = 55$
- $55 – 48 = 7$
- $7 + 13 = 20$
- $20 + 14 = 34$
Result
The final value of the expression is 34.
Thus, the number that will come in place of ‘?’ is 34.
| Step | Expression | Operation | Result |
|---|---|---|---|
| Initial | $21 \text{ A } 34 \text{ C } 6 \text{ B } (72 \text{ D } 9) \text{ A } 13 \text{ B } 1 + (56 \text{ D } 4)$ | Symbol Substitution | $21 + 34 – 6 \times (72 \div 9) + 13 \times 1 + (56 \div 4)$ |
| 1 | $21 + 34 – 6 \times (72 \div 9) + 13 \times 1 + (56 \div 4)$ | Evaluate (72 ÷ 9) and (56 ÷ 4) | $21 + 34 – 6 \times 8 + 13 \times 1 + 14$ |
| 2 | $21 + 34 – 6 \times 8 + 13 \times 1 + 14$ | Evaluate $6 \times 8$ and $13 \times 1$ | $21 + 34 – 48 + 13 + 14$ |
| 3 | $21 + 34 – 48 + 13 + 14$ | Evaluate from left to right | $55 – 48 + 13 + 14$ |
| 4 | $55 – 48 + 13 + 14$ | Evaluate from left to right | $7 + 13 + 14$ |
| 5 | $7 + 13 + 14$ | Evaluate from left to right | $20 + 14$ |
| 6 | $20 + 14$ | Evaluate from left to right | $34$ |
Revision Table: Symbol Substitution and Evaluation
| Symbol | Operation | Value of Expression |
|---|---|---|
| Original | – | $21 \text{ A } 34 \text{ C } 6 \text{ B } (72 \text{ D } 9) \text{ A } 13 \text{ B } 1 + (56 \text{ D } 4)$ |
| Substitution | + – × ÷ | $21 + 34 – 6 \times (72 \div 9) + 13 \times 1 + (56 \div 4)$ |
| Evaluation (Step-by-step) | BODMAS/PEMDAS | $34$ |
Additional Information: Understanding Order of Operations
The order of operations (BODMAS or PEMDAS) is crucial for evaluating mathematical expressions correctly. It ensures that everyone gets the same result for a given expression. Let's quickly review:
- BODMAS: Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction
- PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Division and Multiplication have the same priority and are performed from left to right. Similarly, Addition and Subtraction have the same priority and are performed from left to right.
In this problem, failing to follow the order of operations, especially performing addition or subtraction before multiplication or division (outside of parentheses), would lead to an incorrect answer.
Important Questions from Logical Puzzle
Seven persons P, Q, R, S, T, U and V like different watches namely W1, W2, W3, W4, W5, W6 and W7 (not necessarily in the same order). P and R do not like odd numbered watch. T likes W5. U does not like W2 or W3 or W6 or W7. P likes prime numbered watch. Q likes W4. S likes W2 or W7. Which of the following statement(s) is/are correct ?
I. S likes W7.
II. R likes W2.
III. U likes W1.
IV. V likes W3.
If ‘+’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘–’ and ‘–’ means ‘+’, then
16 + 18 × 3 ÷ 6 = ?
In a certain code language, ‘Today is last match’ is written as ‘Sa Te Mo Pt’, ‘Last king like your team’ is written as ‘De Ra Mo Lo Zs’, ‘Our team won today match’ is written as ‘Te Ra Pt Ae We’. What is the code for ‘Our won is Last’ in that code language?
In a certain code language, ‘LETTER’ is written as ‘ZLZYIO’. What is the code for ‘ACTION’ in that code language?
By interchanging the given two signs, which of the following equations will NOT be correct?
+ and ×
l. 180 - 32 + 3 × 148 ÷ 37 = 88
II. 204 ÷ 17 × 23 + 5 - 97 = 50
