Question

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?

Answer 1

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 ${\displaystyle \frac{x}{2}}$.
So, the correct answer is 2x and the incorrect answer is ${\displaystyle \frac{x}{2}}$.
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.
$\Rightarrow {\displaystyle \frac{x}{2}}=2x-3822$
Now simplify the above equation we have,
$\Rightarrow 3822=2x-{\displaystyle \frac{x}{2}}$
$\Rightarrow 3822={\displaystyle \frac{4x-x}{2}}={\displaystyle \frac{3x}{2}}$
Now multiply by 2 in above equation we have,
$\Rightarrow 3x=2\times 3822=7644$
Now divide by 3 in above equation we have,
$\Rightarrow x={\displaystyle \frac{7644}{3}}=2548$.
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.