Which two numbers from amongst the given options should be interchanged to make the given equation correct? (240 ÷ 2 + 5) × 8 + 15 × 8 = 100
2 and 8
Solving the Equation by Interchanging Numbers
The problem asks us to find which pair of numbers, when swapped in the given equation, makes the equation true. The given equation is:
\[ (240 \div 2 + 5) \times 8 + 15 \times 8 = 100 \]
Our goal is to test the given options and see which interchange results in the Left Hand Side (LHS) of the equation being equal to the Right Hand Side (RHS), which is 100.
Testing the Options for Correct Equation
We will evaluate the equation after performing the interchange suggested by each option.
Option 1: Interchange 2 and 8
If we interchange the numbers 2 and 8 in the original equation, the equation becomes:
\[ (240 \div 8 + 5) \times 2 + 15 \times 2 = 100 \]
Now, let's evaluate the LHS following the order of operations (BODMAS/PEMDAS):
- First, perform the division inside the parenthesis: \(240 \div 8 = 30\).
- Next, perform the addition inside the parenthesis: \(30 + 5 = 35\).
- Now the expression inside the parenthesis is simplified to 35.
- The equation is now: \(35 \times 2 + 15 \times 2 = 100\).
- Perform the multiplications: \(35 \times 2 = 70\) and \(15 \times 2 = 30\).
- The equation is now: \(70 + 30 = 100\).
- Perform the final addition: \(70 + 30 = 100\).
So, the LHS is 100. The RHS is also 100.
Since LHS = RHS (\(100 = 100\)), interchanging 2 and 8 makes the equation correct.
Final Check on Interchanging 2 and 8
After interchanging 2 and 8, the equation becomes \((240 \div 8 + 5) \times 2 + 15 \times 2 = 100\). Calculating the left side gives \((30 + 5) \times 2 + 30 = 35 \times 2 + 30 = 70 + 30 = 100\), which equals the right side. Thus, this interchange makes the equation correct.
Revision Table: Equation Solving Concepts
| Concept | Description |
|---|---|
| Equation | A mathematical statement that two expressions are equal. |
| LHS (Left Hand Side) | The expression on the left of the equals sign. |
| RHS (Right Hand Side) | The expression on the right of the equals sign. |
| BODMAS/PEMDAS | Rules for the order of operations: Brackets/Parentheses, Orders/Exponents, Division/Multiplication (left to right), Addition/Subtraction (left to right). |
Additional Information: Properties of Equations
An equation is like a balance scale; both sides must have the same value to be balanced (true). When we solve equations or check if they are true, we simplify the expressions on both sides according to mathematical rules, like the order of operations.
- Interchanging numbers means swapping their positions within the equation.
- Each interchange changes the value of the expressions involved.
- To check if an interchange works, substitute the numbers and evaluate both sides of the equation.
Similar Questions
If '+' means 'divided by', '-' means 'add', '×' means 'minus' and '÷' means 'multiplied by', then what will be the value of the following expression:
[{(18 × 16) - (5 ÷ 2)} + (5 - 1)] ÷ 1
Which two numbers from amongst the given options should be interchanged to make the given equation correct?
126 ÷ 23 – 138 ÷ ( 5 × 4 – 6) + 4 = 1
If A denotes '+', B denotes '×', C denotes '-’, and D denotes '÷', then what will be the value of the following expression?
124 C 5 B 23 A 56 D 8 = ?
Which of the following interchange of signs would make the given equation correct?
320 × 4 − 16 ÷ 4 + 2 = 18
If A means '+', B means '×', C means '−', and D means '÷', then what is the meaning of '?' in the following equation. What will come in place of ?
(90 C 9) D 9 B 9 A 9 = ?
Which two numbers from amongst the given options should be interchanged to make the given equation correct?
(63 ÷ 9 + 17) ÷ 11 = 15 – 195 ÷ 17 – 2
Which two symbols from amongst the given options should be interchanged to make the given equation correct?
(35 – 2) × 3 = (56 × 8 ÷ 3 + 100) × 11
If A denotes ‘+’, B denotes ‘×’, C denotes ‘−’, and D denotes ‘÷’, then what will come in place of ‘?’ in the following equation?
(9 A 9 C 55 D 5) B ? = 10 B 3 A 5
Which two numbers from amongst the given options should be interchanged to make the given equation correct?
108 ÷ 3 - 126 ÷ ( 5 × 3 + 12) + 4 = 11
In the given question, the statement is followed by two conclusions. Which of the two conclusions is/are true?
Statement: B = T < E ≤ G > F = H > Q
Conclusions:
I. G > Q
II. G > B
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?
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) = ?
