Question

Find the number which when multiplied by $7$ is increased by $78$.

Answer 1

Hint: First we will assume a variable such as $x$, then we will use the given condition as in the question. On applying the given condition we will further equate the conditions so that we can find the required answer. Further we will perform the required operations to find the value of $x$, which will be the required answer to our question.

Complete step by step answer:
Let us assume that the required number be $x$.
So, according to the question, the number when multiplied by $7$ gets increased by $78$.
That is, when we will multiply $x$ by $7$, the number gets increased by $78$, that is, $x$ becomes $x + 78$.
Thus, we can equate these two conditions, that is,
$7x = x + 78$
Now, subtracting $x$ from both sides of the equation, we get,
$ \Rightarrow 7x - x = 78$
$ \Rightarrow 6x = 78$
Now, dividing both sides of the equation by $6$, we get,
$ \Rightarrow x = \dfrac{{78}}{6}$
$ \Rightarrow x = 13$
Therefore, we can say, the number which when multiplied by $7$ gets increased by $78$ is $13$.

Note:
Another way of solving this question is the hit and trial method. In the hit and trial method, we assume a number to be the solution and then apply the conditions as in the question and see if our assumption is correct. But if not correct, then we again assume another number to be the solution and see if the answer is correct. For example, if for the above question, we first assume the answer to be $12$, then apply the given conditions in the question. After we find that $12$ is not the answer, then we assume the answer to be $13$, then on applying the given conditions, we find that it satisfies the condition and hence can say this is the answer.