What will be the value of the given expression if 'A' means '+', 'B' means '-, 'C' means '×', and 'D' means ' ÷ '? 25 В 35 A 12 C 25 D 5 = ?
Solving Expression with Symbol Substitution
The question asks us to find the value of a given expression where letters represent arithmetic operators. We need to substitute the letters with their corresponding operators and then evaluate the resulting mathematical expression following the correct order of operations.
The given substitutions are:
- 'A' means '+' (Addition)
- 'B' means '-' (Subtraction)
- 'C' means '×' (Multiplication)
- 'D' means '÷' (Division)
The expression is given as: $25 \text{ Vcy } 35 \text{ A } 12 \text{ C } 25 \text{ D } 5 = ?$
Looking at the provided mapping, it seems 'Vcy' in the expression is likely a typo and should correspond to one of the given operators. Given the operator 'B' means '-', it is reasonable to assume 'Vcy' is intended to be 'B'. Let's proceed with this assumption.
Substituting the letters with the operators based on the assumption ('Vcy' means '-'):
The expression becomes: $25 - 35 + 12 \times 25 \div 5$
Evaluating the Expression using BODMAS
To evaluate the expression $25 - 35 + 12 \times 25 \div 5$, we must follow the order of operations, often remembered by the acronym BODMAS or PEMDAS.
- Brackets / Parentheses
- Orders / Exponents
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Let's evaluate the expression step-by-step:
- Division: Perform the division operation first. $$12 \times 25 \div 5$$ $$12 \times (25 \div 5)$$ $$12 \times 5$$ The expression is now: $25 - 35 + 12 \times 5$
- Multiplication: Perform the multiplication operation. $$12 \times 5 = 60$$ The expression is now: $25 - 35 + 60$
- Addition and Subtraction: Perform addition and subtraction from left to right. First, subtraction: $$25 - 35 = -10$$ The expression is now: $-10 + 60$ Next, addition: $$-10 + 60 = 50$$
So, the value of the expression $25 \text{ Vcy } 35 \text{ A } 12 \text{ C } 25 \text{ D } 5$, assuming 'Vcy' is 'B', is 50.
Checking the Options
Let's compare our result with the given options:
- Option 1: 45
- Option 2: 50
- Option 3: 55
- Option 4: 40
Our calculated value, 50, matches Option 2.
Revision Table: Operator Substitution & BODMAS
| Symbol | Meaning | Operation |
|---|---|---|
| A | + | Addition |
| B (or Vcy) | - | Subtraction |
| C | × | Multiplication |
| D | ÷ | Division |
BODMAS/PEMDAS Order:
| Order | Operation Type | Notes |
|---|---|---|
| 1 | Brackets/Parentheses | Simplify expressions inside brackets first. |
| 2 | Orders/Exponents | Evaluate powers and roots. |
| 3 | Division and Multiplication | Perform from left to right. |
| 4 | Addition and Subtraction | Perform from left to right. |
Additional Information on Order of Operations
The order of operations is crucial in mathematics to ensure that everyone gets the same result when evaluating an expression. Without a standard order, an expression like $2 + 3 \times 4$ could be interpreted in two ways: $(2 + 3) \times 4 = 5 \times 4 = 20$ or $2 + (3 \times 4) = 2 + 12 = 14$. The BODMAS/PEMDAS rule resolves this ambiguity, stating that multiplication should be done before addition, giving the result 14.
In the case of division and multiplication, or addition and subtraction, the operations are performed from left to right. For example, in $10 \div 2 \times 5$, division is done first ($10 \div 2 = 5$), then multiplication ($5 \times 5 = 25$). If we did multiplication first ($2 \times 5 = 10$), then division ($10 \div 10 = 1$), the result would be different and incorrect according to the standard rule.
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?
