Question

A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer?

Answer 1

Hint: Start by multiplying 7236 by 65, followed by multiplying 7236 by 56. Find the difference between the two results, and the difference is the answer to the above question.

Complete step-by-step answer:
Let us start the solution to the above question by finding the result that the student got, i.e., 7236 multiplied by 65.
 $ \text{Wrong result}=7236\times 65 $
Now, let us find the result that the student would have got if he multiplied 7236 by 56, i.e., the correct result. So, representing this mathematically gives:
 $ \text{Correct result}=7236\times 56 $
Now, to find out how much is the wrong answer greater than the correct one, we will subtract the correct answer from the wrong one. On doing so, we get
 $ \text{Wrong result}-\text{Correct result}=7236\times 65-7236\times 56 $
Now, we will take 7236 common to make the expression less complicated. On doing so, we get
 $ \text{Wrong result}-\text{Correct result}=7236\left( 65-56 \right) $
 $ \Rightarrow \text{Wrong result}-\text{Correct result}=7236\times 9=65124 $
Hence, we can conclude that the wrong result is greater than the wrong result by 65124.

Note: You could have solved the above question by multiplying 7236 with 56 and 65 and finding the exact results and then finding the difference, but that could have included much more calculations and eventually the chances of making a calculation error is higher as more the calculation more the chances of making mistakes. If you have got the difference to be negative, then the negative sign would have indicated that the wrong answer is not greater but less than the correct one.