 Hi, and welcome to the session where we discuss the following question. The question says, P and Q are two unlike parallel forces. When the magnitude of force P is double, it is found that the line of action of force Q is between the lines of action of the new and original resultants. Find the ratio of P and Q. Now, begin with the solution. Then the unlike forces P and Q, A and P. The forces are said to be unlike when they act in opposite parallel direction. Here in this question, we have assumed that unlike forces P and Q acts at point A and P. So these forces will be represented like this. Now, let the resultant of force P and Q point C on A, B produced. Means the resultant will act at this point. This resultant is equal to force Q minus force P. Now, this point divides A, B externally. So we have Q minus P by AB equals to P by BC. Now, this implies BC into Q minus P is equal to P into AB. And this implies B equal to AB by Q minus P into P. Let's name this equation as equation number one. Now, according to the question, when the magnitude of force P is double, it is found that line of action of force Q is midway between the line of action of new and original resultants. That means when this magnitude is double, then force Q is midway between the line of action of the new and original resultant. Now, the resultant of these two unlike forces will be P minus Q. And let us denote this resultant by R dash. Note this point as C dash. So, if magnitude of P is double, the resultant of unlike forces at a point C dash on AB produced. R dash P equals to Q by C dash A equals to P minus Q by AB. Now, this implies C dash B is equal to 2P by 2P minus Q into AB. Let's name this equation as equation number two. Now, since line of action Q is midway between R and R dash, that's original and new resultant dash B is equal to P. Now, from 1 into Q minus P into AB equals to 2P by 2P minus Q into AB. Now, this implies P by Q minus P is equal to 2P minus 2P minus Q. This implies P is equal to 2P minus Q. This implies 4P is equal to 3Q and this implies P is to Q is equal to 3 is to 4. So, ratio of P and Q is 3 is to 4. This is our required answer. So, this completes the session. I am Dave Kao.