What will come in the place of the question mark (?) in the following equation, if '+' and '-' are interchanged and 'x' and '÷' are interchanged?
43 ÷ 13 - 648 × 8 + 52 = ?
588
This problem requires us to solve a mathematical equation after interchanging specific arithmetic symbols according to given rules.
Understanding the Symbol Interchange
The problem states two rules for interchanging symbols:
- The '+' sign is interchanged with the '-' sign.
- The '×' sign is interchanged with the '÷' sign.
Applying the Symbol Changes
The original equation is:
43 ÷ 13 - 648 × 8 + 52 = ?
Let's apply the interchange rules to this equation:
43 ÷ 13becomes43 × 13- 648becomes+ 648× 8becomes÷ 8+ 52becomes- 52
After applying these interchanges, the new equation becomes:
43 × 13 + 648 ÷ 8 - 52 = ?
Solving the Modified Equation
We will now solve the new equation using the standard order of operations (BODMAS/PEMDAS), which stands for Brackets, Orders (powers/roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Step 1: Perform Multiplication and Division
First, we handle the multiplication and division operations from left to right:
- Calculate
43 × 13:$$ 43 \times 13 = 559 $$
- Calculate
648 ÷ 8:$$ 648 \div 8 = 81 $$
Substituting these results back into the equation, we get:
559 + 81 - 52 = ?
Step 2: Perform Addition and Subtraction
Next, we perform the addition and subtraction operations from left to right:
- Calculate
559 + 81:$$ 559 + 81 = 640 $$
- Calculate
640 - 52:$$ 640 - 52 = 588 $$
Final Result
Therefore, the value that comes in place of the question mark (?) after interchanging the symbols is 588.
Important Questions from Mathematical Operations
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 Operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
