What will be the value of the given expression if ‘A’ means ‘+’, ‘B’ means ‘–’, ‘C’ means ‘×’, and ‘D’ means ‘÷’? 50 A 40 B 10 C 12 D 2 = ?
30
Solving the Symbol Substitution Expression
This question requires us to evaluate a mathematical expression where standard arithmetic operators (+, -, ×, ÷) are represented by letters (A, B, C, D). We need to substitute the letters with their corresponding operators and then solve the resulting expression following the correct order of operations.
Understanding the Symbol Substitutions
The question provides the following rules for substitution:
- ‘A’ means ‘+’ (Addition)
- ‘B’ means ‘–’ (Subtraction)
- ‘C’ means ‘×’ (Multiplication)
- ‘D’ means ‘÷’ (Division)
The given expression is:
50 A 40 B 10 C 12 D 2
Rewriting the Expression
Let's replace the letters with their corresponding mathematical operators:
$50 \text{ A } 40 \text{ B } 10 \text{ C } 12 \text{ D } 2 \implies 50 + 40 - 10 \times 12 \div 2$
Applying the Order of Operations (BODMAS/PEMDAS)
To correctly evaluate the expression $50 + 40 - 10 \times 12 \div 2$, we must follow the order of operations. A common acronym for this order is BODMAS or PEMDAS:
- Brackets / Parentheses
- Orders (powers, square roots, etc.) / Exponents
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
In our expression, we have Addition, Subtraction, Multiplication, and Division. According to BODMAS/PEMDAS, we perform Division and Multiplication before Addition and Subtraction.
Step-by-Step Calculation
Let's solve the expression step-by-step:
Expression: $50 + 40 - 10 \times 12 \div 2$
Step 1: Perform Division (from left to right)
We have $12 \div 2$.
$12 \div 2 = 6$
The expression becomes:
$50 + 40 - 10 \times 6$
Step 2: Perform Multiplication (from left to right)
We have $10 \times 6$.
$10 \times 6 = 60$
The expression becomes:
$50 + 40 - 60$
Step 3: Perform Addition and Subtraction (from left to right)
First, perform Addition: $50 + 40$.
$50 + 40 = 90$
The expression becomes:
$90 - 60$
Next, perform Subtraction: $90 - 60$.
$90 - 60 = 30$
The final value of the expression is 30.
Final Value of the Expression
After substituting the symbols and applying the order of operations, the value of the expression 50 A 40 B 10 C 12 D 2 is 30.
Revision Table: Symbol Substitution and Calculation
| Original Expression Part | Substitution Rule | Mathematical Equivalent |
|---|---|---|
| 50 A 40 | A = + | $50 + 40$ |
| 40 B 10 | B = – | $40 - 10$ |
| 10 C 12 | C = × | $10 \times 12$ |
| 12 D 2 | D = ÷ | $12 \div 2$ |
| Step | Operation | Calculation | Expression State |
|---|---|---|---|
| 1 | Initial | $50 + 40 - 10 \times 12 \div 2$ | |
| 2 | Division | $12 \div 2 = 6$ | $50 + 40 - 10 \times 6$ |
| 3 | Multiplication | $10 \times 6 = 60$ | $50 + 40 - 60$ |
| 4 | Addition | $50 + 40 = 90$ | $90 - 60$ |
| 5 | Subtraction | $90 - 60 = 30$ | $30$ |
Additional Information on Order of Operations
The order of operations is a crucial concept in mathematics to ensure consistency in evaluating expressions. Without a standard order, the same expression could yield different results depending on which operation is performed first.
- BODMAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction.
- PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Both acronyms represent the same hierarchy. Multiplication and Division are at the same level, and they should be performed from left to right as they appear in the expression. Similarly, Addition and Subtraction are at the same level and are performed from left to right.
In the given problem, the division ($12 \div 2$) comes before the multiplication ($10 \times 6$) when reading from left to right within that priority level. However, in the expression $10 \times 12 \div 2$, multiplication and division are adjacent. The rule 'from left to right' dictates the order when operators of the same priority level appear consecutively or in a group. In this case, we calculate $12 \div 2$ first, then multiply the result by 10. If it were $10 \div 2 \times 12$, we would calculate $10 \div 2$ first, then multiply by 12.
Important Questions from Logical Puzzle
Below is given a figure, in which a horse is placed on one of the boxes in a square grid of size $5 \times 5$. The horse can move in either of the following ways in a single move:
(i) two boxes to either left or right side and one box to either up or down side
(ii) two boxes to either up or down side and one box to either left or right side
(iii) the horse cannot step on a grey box. The horse has to stay within the grid and any move to out of the grid is NOT legal.
How many white boxes are there which cannot be covered by horse within 3 moves?
- Six persons Raj, Rohit, Rachit, Rajat, Rishu, and Rinku are working in an office. Each of them has a favorite car viz. P, Q, R, S, T, and U, but not necessarily in the same order. Each of them got a different salary - 1000, 2000, 2500, 3000, 3500, and 4000, but not necessarily in the same order. Rajat gets a salary of 2500 and his favorite car is U. The one who likes car Q gets a salary of 3000. Rachit likes car P and gets a salary of 3500. The one who gets a salary of 1000 does not like car R or S. Rinku does not like car Q or S but gets a salary of 2000. Rishu gets a salary of 4000 and does not like a car R. Rohit does not get a salary of 1000. Who gets a salary of 3000?
- Six friends P, Q, R, S, T, and U are sitting at different positions in a row of the company, and each of them get a different salary viz – 500, 800, 1000, 1500, 1800 & 2000, but not necessary in the same order. The friend who gets a salary of 2000 does not sit at the extreme end of the row. Q sits immediately before R and gets a salary of 800. T sits between U and S. Q is second to the left of S. P sits at the left end of the row and gets a salary of 1000. T gets a salary of 1500. R gets a salary neither of 2000 nor of 1800. How much salary does U get?
- Seven men A, B, C, D, E, F and G are standing in a queue, one behind the other in that order. That is, A is first in queue while G brings up the rear. Each of them is wearing a hat of a different colour of the rainbow - Violet, Indigo, Blue, Green, Yellow, Orange, and Red, but not necessarily in that order. It is also known that:
• D can see in front of him green and blue hats, but not the violet hat.
• E can see violet and yellow hats, but not the red hat.
• G can see hats of all the colours except Orange.
• E is wearing the Indigo coloured hat.
What colour hat is worn by F? - Who amongst the females arrived third?
