Let the required number be x.
Given that, when multiplied by 7, it gives 7x, and x increases by 78.
According to the question we can write as 7x = x + 78
Transposing x to LHS, we get
⇒ 7x – x = 78
⇒ 6x = 78
Dividing both sides by 6, we get
⇒ 6x/6 = 78/6
⇒ x =13
Thus, the required number is x = 13.
