EVERYDAY MATHEMATICS

In a bangle shop, if the shopkeeper displays the bangles in the form of a square then he is left with $38$ bangles. If he wanted to increase the size of square by one unit each side of the square, he found that $25$ bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was _______.

In the Maths Olympiad of $2020$ at Animal Planet, two representatives from the donkey’s side, while solving a quadratic equation, committed the following mistakes.
(i) One of them made a mistake in the constant term and got the
roots as $5$ and $9$.
(ii) Another one committed an error in the coefficient of $x$ and he
got the roots as $12$ and $4$.
But in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the quadratic equation.

$₹6500$ were divided equally among a certain number of people. If there had been $15$ more people, each would have got $₹30$ less. Find the original number of people.

Swati can row her boat at a speed of $5$ km/hr in still water. If it takes her $1$1 hour more to row the boat $5.25$ km upstream than to return downstream, find the speed of the stream.