# Suraj was asked to multiply a number by 2, but by mistake, he divided the number by 2. If his answer was less than the correct answer by 3822, what was the number?

Last updated date: 18th Mar 2023

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Answer

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Hint – In this question Suraj performed a mistake in mathematical operation instead of multiplying by 2, he divided the number by 2. So firstly let the number be a variable and use the condition given in the question that his incorrect answer is less than the correct answer by 3822 to find this required variable.

Complete step-by-step solution -

Let the number be x.

Now Suraj was asked to multiply the number by 2, so the number becomes 2x.

Now, but by mistake he divides the number by 2 so, the number becomes $\dfrac{x}{2}$.

So, the correct answer is 2x and the incorrect answer is $\dfrac{x}{2}$.

Now it is given that his answer was less than the correct answer by 3822.

Therefore the incorrect answer is less than the correct answer by 3822.

$ \Rightarrow \dfrac{x}{2} = 2x - 3822$

Now simplify the above equation we have,

$ \Rightarrow 3822 = 2x - \dfrac{x}{2}$

$ \Rightarrow 3822 = \dfrac{{4x - x}}{2} = \dfrac{{3x}}{2}$

Now multiply by 2 in above equation we have,

$ \Rightarrow 3x = 2 \times 3822 = 7644$

Now divide by 3 in above equation we have,

$ \Rightarrow x = \dfrac{{7644}}{3} = 2548$.

So the number is 2548.

So, this is the required answer.

Note – Whenever we face such types of problems the key concept is to use the questions information which is being provided to form a mathematical relation between the incorrect answer obtained and the correct answer which needs to be there. This concept will help you get on the right track to reach the answer.

Complete step-by-step solution -

Let the number be x.

Now Suraj was asked to multiply the number by 2, so the number becomes 2x.

Now, but by mistake he divides the number by 2 so, the number becomes $\dfrac{x}{2}$.

So, the correct answer is 2x and the incorrect answer is $\dfrac{x}{2}$.

Now it is given that his answer was less than the correct answer by 3822.

Therefore the incorrect answer is less than the correct answer by 3822.

$ \Rightarrow \dfrac{x}{2} = 2x - 3822$

Now simplify the above equation we have,

$ \Rightarrow 3822 = 2x - \dfrac{x}{2}$

$ \Rightarrow 3822 = \dfrac{{4x - x}}{2} = \dfrac{{3x}}{2}$

Now multiply by 2 in above equation we have,

$ \Rightarrow 3x = 2 \times 3822 = 7644$

Now divide by 3 in above equation we have,

$ \Rightarrow x = \dfrac{{7644}}{3} = 2548$.

So the number is 2548.

So, this is the required answer.

Note – Whenever we face such types of problems the key concept is to use the questions information which is being provided to form a mathematical relation between the incorrect answer obtained and the correct answer which needs to be there. This concept will help you get on the right track to reach the answer.

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