Solving for the Initial Number
Let the initial number be represented by the variable $x$.
Atul's Calculation
Atul first squared the initial number, resulting in $x^2$. Then, he subtracted $15$ from it. His result is:
$x^2 - 15$
Pratul's Calculation
Pratul first subtracted $15$ from the initial number, giving $(x - 15)$. He then squared this difference. His result is:
$(x - 15)^2$
Equating the Results
The problem states that both Atul and Pratul obtained the same answer. Therefore, we can set their results equal to each other:
$x^2 - 15 = (x - 15)^2$
Step-by-Step Equation Solution
- Expand the right side of the equation: $(x - 15)^2 = x^2 - 2(x)(15) + 15^2 = x^2 - 30x + 225$.
- Substitute the expanded form back into the equation: $x^2 - 15 = x^2 - 30x + 225$.
- Subtract $x^2$ from both sides: $-15 = -30x + 225$.
- Add $30x$ to both sides: $30x - 15 = 225$.
- Add $15$ to both sides: $30x = 225 + 15$.
- Simplify: $30x = 240$.
- Divide by $30$: $x = \frac{240}{30}$.
- Calculate the final value: $x = 8$.
The initial number is $8$.
Similar Questions
- What will come in the place of the question mark (?) in the following equation, if '+' and '−' are interchanged and '×' and '÷' are interchanged?
65 × 5 − 19 ÷ 3 + 25 = ? - What will come in place of the question mark (?) in the following equation if '×' and '+' are interchanged and '−' and '÷' are interchanged?
32 ÷ 2 × 72 − 9 + 5 = ? - If 'A' stands for '÷', 'B' stands for '×', 'C' stands for '+' and 'D' stands for '−', what will come in place of the question mark (?) in the following equation?
7 B 5 D 48 A 4 C 13 = ? - What will come in the place of the question mark (?) in the following equation, if ‘+’ and ‘÷’ are interchanged, and ‘−’ and ‘×’ are interchanged?
6 + 3 ÷ 48 − 4 × 25 = ? - Which two signs are to be interchanged to make the given equation correct?
$15 - 3 \div 40 + 5 \times 30 = 23$ - What will come in the place of the question mark (?) in the following equation, if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
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Important Questions from Mathematical Operations
What will come in the place of ‘?’ in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
18 ÷ 9 + 24 × 3 − 16 = ?If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’, and ‘D’ stands for ‘−’, what will come in place of the question mark (?) in the following equation?
88 B 3 D 12 A 4 C 6 = ?Select the set in which the numbers are related in the same way as are the numbers of the given sets.
(NOTE: Operations should be performed on whole numbers without breaking down the numbers into their 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.)
Given sets:
(9, 21, 193)
(12, 15, 184)What will come in the place of the question mark (?) in the following equation, if ‘÷’ and ‘+’ are interchanged and ‘−’ and ‘×’ are interchanged?
44 ÷ 78 + 6 − 3 × 19 = ?Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
